Definite
∫(5x + 10) dx
lower limit: 0
upper limit: 7
no need to simplify, no calculator
[5(7)2]/2 + 70
∫sec2x dx
tanx + C
∫lnx dx
xln(x) − x + C
Given that the particle's velocity on the x-axis is modeled by a differential equation dx/dt = x2 + 4x and given that x(2) = 5, find the particle's position at x = 0.
5 - (8/3) - 8
Which country uses this flag?
https://drive.google.com/file/d/1mZ65g--o6cG1JV_PK35qrVo2q7NH1w9e/view?usp=sharing
Bhutan
∫1/(1+x2) dx
lower limit: 0
upper limit: 1
No calculator, fully simplify
π/4
∫(csc 5x cot 5x)dx =
-(csc5x/5) + C
∫ xex dx
xex - ex + C
For r = 2Ѳ cos Ѳ, write the integral in order to find the area of the polar function from 0 < x < π/2 but do not evaluate.
1/2 ∫ (2Ѳ cos Ѳ)2 dѲ from 0 to π/2
(2/3)(493/2) - (1/14)(492)
∫(tanx) dx
lower limit:2
upper limit: 3
No need to fully simplify, no calculator.
-ln|cos3| + ln|cos2|
∫(5/(x2 +5x+6)) dx
5 ln |x+2| - 5 ln |x+3| + C
∫13x3(-cosx) dx
-13x3sinx - 39x2cosx + 78xsinx + 78cosx + C
find the particular solution of dy/dx = cos x / y2 with x = 0 and y = -1
y3 = 3sinx - 1
∫cotx dx
ln|sinx| + C
∫1/(x)(sqrt x2- 9) dx
Lower limit: 5
Upper limit: 7
No need to fully simplify, no calculator
(1/3)arcsec|7/3| - (1/3)arcsec|5/3|
∫(x+2)/(x+7) dx
x+7-5ln|x+7| + C
∫exsinxdx
(exsinx-excosx)/2
Given the differential equation
dy/dx = (3x3 + 7x2 + 5)(y-3) and the point (0,1), find function y in terms of x
y = -2e(3/4)x^4 + (7/3)x^3 + 5x + 3
∫secx dx + ∫cscx dx
Lower limit for both: 2
upper limit for both: 3
ln|sec3 + tan3| - ln|sec2-tan2| - ln|csc3 - cot3| + ln|csc2 + cot2|
∫|2x-5| dx
lower limit: -5
upper limit: 10
No calculator, give a fully simplified fraction or decimal.
112.5 or 225/2
∫(x3 +6x2+13x+7)/(x+2) dx
1/3 x3 +2x2 + 5x - 3ln|x+2| + C
∫e^(x+27)*cos(x)dx
1/2(ex+27(sinx + cosx)) + C
Given that dy/dx = (7x2-9x+3)(y-3) find y given that y(0)=6
y=3e(7/3)x^3+(9/2)x^2+3x+3
∫1/(x-1) dx
From 0 to 5
ln 4 or diverges