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

The region under y = √(x) from x = 0 to x = 2 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(x)0 ≤ x ≤ 2

V =

2.Easy

Evaluate I = ∫₀¹ x·e^2x dx.

∫₀¹ x·e^2x dx

I =

3.Medium

Evaluate I = ∫₀² e^2x dx.

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

I =

4.Medium

Evaluate I = ∫₁² x·ln x dx.

∫₁² x ln x dx

I =

5.Hard

Evaluate I = ∫₀^1.5 x²·eˣ dx.

∫₀^1.5 x²eˣ dx

I =

6.Hard

Evaluate I = ∫₀³ x²·eˣ dx.

∫₀³ x²eˣ dx

I =

Answer key

1. V = 6.283
2. I = 2.097
3. I = 26.8
4. I = 0.6363
5. I = 3.602
6. I = 98.43

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