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 = ∫₋₁⁰ (x³ − 3x − 3) dx.

f(x) = x³ − 3x − 3[−1, 0]

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 = ∫₀³ e^0.5x dx.

f(x) = e^0.5x[0, 3]

I =

4.Medium

Evaluate I = ∫₂⁶ 4/x dx.

f(x) = 4/x[2, 6]

I =

5.Hard

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

y = 2xy = 2x²

V =

6.Hard

Evaluate I = ∫₀^2.5 x²·eˣ dx.

∫₀^2.5 x²eˣ dx

I =

Answer key

1. I = −1.75
2. V = 3.142
3. I = 6.963
4. I = 4.394
5. V = 1.676
6. I = 37.59

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