Integrals worksheet with answers

Free printable Integrals worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheet Practise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________ Date: ____________

1.Easy

Evaluate I = ∫₀³ (x³ + x + 3) dx.

f(x) = x³ + x + 3[0, 3]

I =

2.Easy

The region under y = √(2x) from x = 0 to x = 1 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(2x)0 ≤ x ≤ 1

V =

3.Medium

Evaluate I = ∫₀² e^−0.5x dx.

f(x) = e^−0.5x[0, 2]

I =

4.Medium

Evaluate I = ∫₀¹ e^0.5x dx.

f(x) = e^0.5x[0, 1]

I =

5.Hard

Find the area A of the region enclosed by y = 0.5x² and y = 2x.

y = 0.5x²y = 2x

A =

6.Hard

Evaluate I = ∫₀^1.5 x²·eˣ dx.

∫₀^1.5 x²eˣ dx

I =

Answer key

1. I = 33.75
2. V = 3.142
3. I = 1.264
4. I = 1.297
5. A = 5.333
6. I = 3.602

Full step-by-step solutions: practise this topic on examproblems.com.