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 = ∫₋₁¹ (−4x² + 3x + 5) dx.

f(x) = −4x² + 3x + 5[−1, 1]

I =

2.Easy

Evaluate I = ∫₀^1.5 x·e^−x dx.

∫₀^1.5 x·e^−x dx

I =

3.Medium

Evaluate I = ∫₀^π/3 x·cos x dx (x in radians).

∫₀^π/3 x·cos x dx

I =

4.Medium

Evaluate I = ∫₀^π/2 x·sin x dx (x in radians).

∫₀^π/2 x·sin x dx

I =

5.Hard

Evaluate I = ∫₀² x²·eˣ dx.

∫₀² x²eˣ dx

I =

6.Hard

The region between the line y = 4x and the parabola y = 2x² is rotated about the x-axis. Find the volume V of the solid.

y = 4xy = 2x²

V =

Answer key

1. I = 7.333
2. I = 0.4422
3. I = 0.4069
4. I = 1
5. I = 12.78
6. V = 53.62

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