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 = ∫₀³ (−4x² + 3x + 8) dx.

f(x) = −4x² + 3x + 8[0, 3]

I =

2.Easy

The region under y = √(x) from x = 0 to x = 4 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(x)0 ≤ x ≤ 4

V =

3.Medium

Evaluate I = ∫₀² x·sin x dx (x in radians).

∫₀² x·sin x dx

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

Find the area A of the region enclosed by y = 0.5x² and y = 4x.

y = 0.5x²y = 4x

A =

Answer key

1. I = 1.5
2. V = 25.13
3. I = 1.742
4. I = 1.718
5. I = 0.0609
6. A = 42.67

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