Practice Integral in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The reverse operation of differentiation; it also computes the exact area under a curve between two points.

If derivative gives rate, integral gives total. Derivative of position = velocity; integral of velocity = position.

Showing a random 20 of 50 problems.

Example 1

medium
Find ∫sin⁡x dx.

Example 2

easy
Find ∫(4x3+6x) dx

Example 3

easy
Find ∫x5 dx.

Example 4

easy
Evaluate ∫032x dx.

Example 5

medium
Find ∫(x2−4x+5) dx.

Example 6

medium
Find ∫1x3 dx.

Example 7

easy
Find ∫3 dx.

Example 8

challenge
Find ∫(x+1)2 dx by expanding first.

Example 9

easy
Find ∫x2 dx.

Example 10

easy
Find ∫x3 dx.

Example 11

easy
Find ∫4x3 dx.

Example 12

medium
Find ∫(x3+3x2−2x+1) dx.

Example 13

easy
Find ∫(5x2−3x+7) dx

Example 14

medium
Find ∫(2ex+3cos⁡x) dx.

Example 15

hard
A particle has velocity v(t)=3t2−6t m/s. Find its displacement from t=0 to t=4.

Example 16

hard
Find ∫xex2 dx.

Example 17

easy
Find ∫(2x+1) dx.

Example 18

hard
Evaluate ∫01(3x2+2x+1) dx.

Example 19

easy
Find ∫cos⁡x dx.

Example 20

medium
Evaluate ∫−11(x3+x) dx.