June 27, 20XX
Jolting down, touring, and seeing more memorabilia and advertisements on the main side's walls with lots of key sentences and quotes:
"A collection of three classic 3D games!"
"A multiplayer online game where players compete against each other in a battle royale-style format!"
"An augmented reality racing game. Players control a physical kart equipped with a camera, which interacts with the game!"
"Players navigate through various 3D platforming levels in both single-player and multiplayer modes!"
"A golf sports game featuring various Mario characters. Players compete in golf tournaments and can use special abilities and power-ups to gain an advantage on the course"
"A party game compilation that brings back classic boards and minigames. It includes online multiplayer and offers a nostalgic experience for fans!"
"A soccer game that offers a fast-paced and action-packed take on the sport, with power-ups and special moves available to players!"
"A rabbits-themed game made in a tactical role-playing game!"
"An upcoming platformer game!"
"An announced remake of the original classic and will offer an updated version of the beloved role-playing game!"
"Mario and Sonic participate in Operation Amiga"
"Educational game developed for students!"
"Puzzle game where players assume different colored characters of blue, red, and yellow!"
"Employee Hirings at Popful Mail Post Office!"
"An educational adventure for a all ages!"
"Invitation to the Crackers' Studium Stadium's Grand Opening!"
"All ages for an X-treme game!"
"Extreme game for all ages!"
"Marketing for DS consoles!"
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...