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

The region under y = √(x) from x = 0 to x = 4 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(x)0 ≤ x ≤ 4

V =

2.Easy

Evaluate I = ∫₀^1.5 x·e^x/2 dx.

∫₀^1.5 x·e^x/2 dx

I =

3.Medium

Evaluate I = ∫₀² e^0.5x dx.

f(x) = e^0.5x[0, 2]

I =

4.Medium

Evaluate I = ∫₀¹ e^x dx.

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

I =

5.Hard

Evaluate I = ∫₀² x²·eˣ dx.

∫₀² x²eˣ dx

I =

6.Hard

The region between the line y = 6x and the parabola y = 2x² is rotated about the x-axis. Find the volume V of the solid.

y = 6xy = 2x²

V =

Answer key

1. V = 25.13
2. I = 1.883
3. I = 3.437
4. I = 1.718
5. I = 12.78
6. V = 407.2

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