Integration

Practice Questions

Calculus 3 › Integration

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1

If the velocity function of a car is , what is the position when ?

2

Calculate $\int_0^{\infty} 2xe^{-x} dx$

3

Calculate antiderivative of $f(x)=\frac{3x^2+2x+1}{x^3+x^2+x+1}$

4

The acceleration of an object is given by the equation . What is the equation for the position of the object, if the object has an initial velocity of and an initial position of ?

5

The velocity equation of an object is given by the equation . What is the position of the object at time if the initial position of the object is ?

6

Consider the velocity function given by :

Find the position of a particle after seconds if its velocity can be modeled by and the graph of its position function passes through the point .

7

Calculate $\int \cos (x) e^{sin(x)}dx$ .

8

$\int \frac{2t-1}{t^2+4}dt$

9

Evaluate the following integral:

$\int\sin^3 x\cot^2 x dx$

10

Calculate $\int \cos \theta \left( 2 \sin \theta+5\right )^3 d \theta$

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