Properties of Definite Integrals Worksheet with Answer Key

What's on the worksheet

1. The functions f and g are continuous, with $\int_{-1}^{4} f
   \int_{-1}^{4} \big(2f(x) - 5g(x)\big)\,dx\int_{-1}^{2} f(x)\,dx\int_{3}^{3} f(x)\,g(x)\,dx\int_{-1}^{4} \big(f(x) - 2g(x) - x\big)\,dx\int_{4}^{2} \big(6 - f(x)\big)\,dx
2. Find the least value m and the greatest value M of each integrand on its interval, then use $m(b - a) \le \int_a^b f
   \int_1^4 \dfrac{12}{x + 2}\,dx\int_{-1}^{2} \dfrac{6}{x^2 + 2}\,dx\int_0^2 \sqrt{x^3 + 1}\,dx\int_{-2}^{1} \left(x^2 + 2x + 3\right)dx
3. A continuous function f has $\int_{-3}^{2} f
4. The function f is odd and g is even, both continuous on [-3, 3].
5. Use the comparison properties.
6. x y 2 4 6 8 −2 2 4 y = f