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 lower and upper bounds, yielding a single numerical value rather than a function.
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.