June 26, 20XX
Jolting down, touring, and seeing more memorabilia and advertisements on the northern side's walls with lots of key sentences and quotes:
"Mario and his friends in a virtual board game adventure"
"Embark on a role-playing puzzle journey that combines the worlds of Puzzle & Dragons!"
"Dr. Mario in a guest lecture on how to eliminate viruses"
"Create and play your own 2D platforming levels in this innovative game that lets you unleash your creativity!"
"Mario and his pals in an exciting sports experience"
"Team up in a hilarious and action-packed role-playing adventure!"
"Guide a cast of characters through puzzling levels using the power of Amiibo figures!"
"Mario, Sonic, and their friends as they compete in various Olympic sports events"
"Immerse yourself in a creative sandbox world where you can build, explore, and survive in a virtual universe!"
"Mario on an adventure journey to restore color to Prism Island and unravel its mysteries"
"Mario and friends race against each other in a variety of mini-games and challenges"
"Design and play your own 2D levels on the go, sharing them with others and tackling creative challenges"
"Control continuous auto-running adventure in this mobile platformer, collecting coins, jumps over obstacles, and defeat enemies"
"Compete in a variety of sports including soccer, baseball, tennis, golf, and horse racing with your characters"
"Race against friends or opponents in exhilarating kart races, featuring new tracks, characters, and multiplayer modes!"
"Dive into the expansive world on this game, where you can build, explore, and survive in a blocky sandbox environment!"
"Experience the thrill in virtual reality, as you race against opponents in immersive arcade gameplay!"
"Enjoy a compilation of classic arcade games"
"Mario and the Rabbit creatures"
"Mario and Luigi as they team up to save the Beanbean Kingdom"
"Mario and his new ally, Cappy, in an epic adventure to rescue Princess Peach from Bowser"
"Relive the best mini-games as you compete with friends in this compilation party game"
"Engage in intense tennis matches!"
"Gather your friends and family for a lively party experience filled with mini-games, strategic board gameplay, and cooperative team modes!"
"Luigi as he explores a haunted mansion, using his trusty Poltergust 3000 to capture the Boos and rescue his brother Mario"
"Mario faces off in a chaotic and action-packed fighting"
"Delve into the comical world adventure!"
"Run, jump, and save Princess Peach in this classic 2D platformer, featuring new levels, power-ups, and multiplayer modes"
"Unleash your creativity by designing and sharing your own 2D levels, or play through a vast collection of user-created levels!"
"Dr. Mario and his friends in virus research labs"
"Experience the exhilarating racing action!"
"Luigi on a thrilling action-adventure as he explores a haunted hotel, armed with the Poltergust G-00, to rescue his friends from the clutches of the mischievous King Boo"
"Mario, Sonic, and their friends, bringing the excitement of the Japanese-themed Olympics"
"Mario sets out to save Princess Peach and unravel the mystery of the origami menace threatening the Mushroom Kingdom"
"Sonic and his friends as they battle against the villainous Lyric"
"Sonic and his pals as they navigate challenging levels and uncover the secrets behind the shattered crystal"
"Sonic, Tails, Knuckles, and other characters in this endless runner contest"
"Sonic and his friends race against time to save their islands' home"
"Sonic in a patrol car and chase after Dr. Robotnik"
"Sonic with Mighty the Armadillo and Ray the Flying Squirrel"
"Sonic and his friends pilot spaceships to defend against enemy forces"
"Sonic in popcorn shop"
"Sonic and his friends battling each other in intense one-on-one fighting practice"
"Sonic participating in various athletic events, including running and jumping"
"This educational game aimed at children features various mini-games and activities!"
"Tails creating music using different instruments"
"This educational game takes place in a school setting and helps children learn subjects like math and language through activities and puzzles!"
"Tennis matches with Sonic and others"
"Playing golf with Sonic"
"The peaceful activity of fishing with Sonic and trying to catch different aquatic creatures"
"A game of billiards with Sonic and others"
"The Chao creatures being interacted with friends"
"Bowling matches with Sonic"
"The thrill of high-speed racing with Sonic and friends"
"This game provides players with exciting kart racing action!"
"Sonic on a vertical jumping adventure, avoiding obstacles and enemies"
"A mobile game offering fast-paced kart racing in a 3D environment!"
"High-speed racing with Sonic and others"
"Casino poker with the Sonic and others"
"Sonic through vertical jumping challenges and aiming for high scores"
"Players must strategically clear blocks by matching them to score points and progress through the game!"
"A pinball-themed game for all ages!"
"Dr. Robotnik's Mean Bean Machine's prisoners being rescued"
"Tails with his Skypatrol"
"Tails on his adventure"
"An isometric puzzle game for all ages!"
"Players compete in a board game-like setting with various shuffling mini-games!"
"A pinball gameplay for all ages!"
"Players engage in battles using a combination of moves and special attacks!"
"Sonic and his allies in turn-based battles and explore a mystery involving the Dark Brotherhood"
"Sonic as he runs through various stages, collecting rings and avoiding obstacles"
"An arcade-style jumping game where players to climb as high as possible and achieve high scores!"
"Players run through levels, collect rings, and defeat enemies while trying to achieve the highest score!"
"Sonic, Tails, and Knuckles as they race through levels, collecting rings and defeating enemies"
"Sonic with the help of Mario face off against one of Dr. Eggman's unit leaders; Infinite"
"Mario and Luigi with Yoshi on high-speed adventures with Sonic and his friends"
"Tails, Barry, and Shadow solving a murder mystery in a train express"
"A gaming compilation that includes three games for all ages!"
"A gaming compilation that includes ages 12 and up!"
"A gaming compilation that includes ages 13 and up!"
"A gaming compilation that includes ages 14 and up!"
"Sonic viewing the museum's Gems Collection"
"The museum releasing Ultimate Genesis Collection"
"Video game designers announcing the PC Video Game Consoles' Collection"
"Video game designers announcing the Classic Video Game Consoles' Collection"
"Video games designers discussing the origins of their gaming products"
Math Notes: (filled with academic musings)
Integral pi/2,0 (7 sin x - 2 cos x) dx
(-7 cos x - 2 sin x) | pi/2,0
(-7 cos (pi/2) - 2 sin (pi/2)) - (-7 cos (0) - sin (0))
= -2 - (-7)
= 5
If a polynomial; use the power rule: #(n^x+1 / x+1)
Integral 1,0 3(4x+x^4)(10x^2 + x^5 -2)^6 dx
u=10x^2 + x^5 - 2
du/dx = 20x + 5x^4
du/dx = 5(4x + x^4)
dx = du / 5(4x+x^4)
Integral 1,0 3(4x+x^4) u (du / 5(4x+x^4))
3/5 Integral udu = 3/5 (u^2 / 2) |1,0
= 3/10 (10x^2 + x^5 - 2) |1,0
If a polynomial; use the power rule: #(n^x+1 / x+1)
Integral 1,0 3(4x+x^4)(10x^2 + x^5 - 2)^6 dx
Integral 1,0 3(4x+x^4)(u)^6
dx (du/dx) = 20x + 5x^4 dx
du/(20+5x^4) = (20x+5x^4) dx / 20x + 5x^4
dx = du / 20x+5x^4
Integral 1,0 3(4x+x^4) u^6 du/20x+5x^4
Multiply 1/5 and 5
1/5 Integral 1,0 (5)(3)(4x-x^4)u^6 du/20x+5x^4
3/5 Integral 1,0 (20x-5x^4)u^6 / 20x-5x^4 du
3/5 Integral 1,0 u^6 du
3/5 Integral 1,0 (u^7 / 7) du
Using Power Rule
3/5 (u^7 / 7)
=3/35 (10x^2 + x^5 - 2)^7 |1,0
=3/35 (10(1)^2 + (1)^5 - 2)^7
=409,979.7478
Integral pi/4, 0 8cos(2t) / square root 9-5sin(2t)
Find the U-Sub
u=9-5sin(2t)
du/dt
Integral 1/u^1/2
Integral u^-1/2 du
u= 9-5sin(2t)
du= 9-5sin(2t)
du/dt= -5cos(2t)
Integral pi/4, 0 8cos(2t) / (square root u) dt
Chain Rule
dt (du/dt) = -5cos(2t)(2) dt
dt=du/-10cos(2t)
du/-10cos(2t) = -10cos(2t) / -10cos(2t) dt
Integral pi/4, 0 8cos(2t)/square root u (du/-10cos(2t))
8 Integral pi/4, 0 -10cos(2t)/square root u (du/-10cos(2t))
(-1/10)(8/1) Integral pi/4, 0 -10cos(2t)/square root u (du/-10cos(2t))
-8/10 Integral pi/4, 0 du/square root u
-8/10 Integral pi/4, 0 u^-1/2 du
-8/10 (u^-1/2+1 / -1/2+1) du |pi/4, 0
-8/10 (u^1/2)/(1/2) du |pi/4, u
-8/5 (9-5sin(2t))^1/2 |pi/4, 0
-8/5 (9-5sin(pi/4))^1/2
-8/5 (9-5sin(0))^1/2
=1.059...
Integral 4,1 square root w(e)^1-square root w^3 dw
u=1-square root 1-square root w^3
du=1-square root w^3
dw(du/dw) = -3/2(w^1/2) dw
du/-w = -3/2(w^1/2) dw / -3/2w^1/2
dw = du / -3/2 w^1/2
Integral 4,1 square root w(e)^u du/(-3/2 (w^1/2))
Integral 4,1 square root w(e)^u du(-3/2 (square root w))
-2/3 Integral 4,1 e^u du/(-3/2)
-2/3 Integral 4,1 e^u du
-2/3 (e^u) |4,1
-2/3 e^1-square root w^3 |4,1
(-2/3 e^1-square root 4^3) - (-2/3 e^1-square root 1^3)
=0.66...