Practice Definite Integral in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
An integral evaluated between specific bounds a and b, yielding a single number: the signed area under the curve.
The signed total area under the curve from a to b—positive above the x-axis, negative below.
Example 1
easyEvaluate \int_1^4 (2x - 1)\,dx.
Example 2
mediumEvaluate \int_{-1}^{2} (x^2 - x)\,dx and interpret the sign of the result.
Example 3
easyEvaluate \int_0^3 x^2\,dx.
Example 4
hardEvaluate \int_0^{\pi} \sin x\,dx and explain the geometric meaning.