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 = ∫₋₂¹ (4x² + 3x − 2) dx.

f(x) = 4x² + 3x − 2[−2, 1]

I =

2.Easy

Evaluate I = ∫₋₁² (−3x² − 3x) dx.

f(x) = −3x² − 3x[−1, 2]

I =

3.Medium

Evaluate I = ∫₁³ 1/x dx.

f(x) = 1/x[1, 3]

I =

4.Medium

Evaluate I = ∫₀¹ e^x dx.

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

I =

5.Hard

Evaluate I = ∫₀^0.5 x²·eˣ dx.

∫₀^0.5 x²eˣ dx

I =

6.Hard

The region between the line y = 4x and the parabola y = 3x² is rotated about the x-axis. Find the volume V of the solid.

y = 4xy = 3x²

V =

Answer key

1. I = 1.5
2. I = −13.5
3. I = 1.099
4. I = 1.718
5. I = 0.0609
6. V = 15.89

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