Integration Theory

Question 1

If f ‘(x) = g(x) what is the antiderivative of g(x)?

Answer 1

f(x)+C

Question 2

What is ∫ 𝑒^𝑥 𝑑𝑥?

Answer 2

e^x + C

Question 3

What is ∫ sin(𝑥) 𝑑𝑥?

Answer 3

-cos(x) + C

Question 4

What is ∫ cos(𝑥) 𝑑𝑥?

Answer 4

sin x + C

Question 5

What is ∫ 1/𝑥 𝑑𝑥

Answer 5

ln|x| + C

Question 6

What is ∫ sec(𝑥) tan(𝑥) 𝑑𝑥?

Answer 6

sec x + C

Question 7

What is ∫ sec^2 (𝑥) 𝑑𝑥?

Answer 7

tan x + C

Question 8

What is ∫ 4𝑥^5 𝑑𝑥?

Answer 8

2/6 x^6 + C

Question 9

What is ∫ 3𝑥^-7𝑑𝑥?

Answer 9

− 1/2 𝑥^−6 + 𝐶

Question 10

What’s the antiderivative of velocity?

Answer 10

Position

Question 11

What’s the antiderivative of acceleration?

Answer 11

Velocity

Question 12

Knowing the force, what’s the acceleration?

Answer 12

a = F/m

Question 13

What is ∫ 1/(1+𝑥^2) 𝑑𝑥?

Answer 13

arctan(𝑥) + 𝐶

Question 14

What is ∫ 1/(√1−𝑥^2) 𝑑𝑥?

Answer 14

arcsin(x)+C

Question 15

What is ∫ 1/(|𝑥|√𝑥^2 −1) 𝑑𝑥?

Answer 15

arcsec(𝑥) + 𝐶

Question 16

What is Area’?

Answer 16

f(x)

Question 17

if the area under a graph is x^3, what’s the function?

Answer 17

f(x) = 3x^2

Question 18

If A(x) = f(x) then what is A(x)?

Answer 18

The antiderivative of f(x)

Question 19

Let A(x) be the area from 2 to x under f(x). If A(x) = F(x) + C, what is C?

Answer 19

-F(2)

Question 20

What is (2x+1)|5
|2

Answer 20

(2 × 5 + 1) − (2 × 2 + 1) = 6