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.

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1.Easy

Evaluate I = ∫₁² (4x³ + x − 4) dx.

f(x) = 4x³ + x − 4[1, 2]

I =

2.Easy

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

y = √(x)0 ≤ x ≤ 1

V =

3.Medium

Evaluate I = ∫₁² 2/x dx.

f(x) = 2/x[1, 2]

I =

4.Medium

Evaluate I = ∫₁^2.5 x·ln x dx.

∫₁^2.5 x ln x dx

I =

5.Hard

The region between the line y = 3x and the parabola y = 3x² is rotated about the x-axis. Find the volume V of the solid.

y = 3xy = 3x²

V =

6.Hard

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

y = xy = x²

V =

Answer key

1. I = 12.5
2. V = 1.571
3. I = 1.386
4. I = 1.551
5. V = 3.77
6. V = 0.4189

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