8. Definite Integrals

Find ${\int }_0^{6}f\left(x\right)dx$ given the graph of $y=f\left(x\right)$.

Express the following limit as a definite integral on the interval $[0,10]$.

${\lim }_{n\to \infty }{\sum }_{k=1}^n{(x_k^{\ast }-3)}^2\Delta x$

Given the following definite integral of the function $f\left(x\right)=3x^2-2x$, write the simplified integral:

$-\int_4^0\!f\left(x\right)\,dx$

Write the two definite integrals subtracted below as a single integral.

${\int }_1^6\sqrt{x^2-5x}dx-{\int }_{10}^6\sqrt{x^2-5x}dx$

7–64. Integration review Evaluate the following integrals.

12. ∫ from -5 to 0 of dx / √(4 - x)

7–64. Integration review Evaluate the following integrals.

24. ∫ from 0 to θ of (x⁵⸍² - x¹⸍²) / x³⸍² dx

7–84. Evaluate the following integrals.

19. ∫ from 0 to π/2 [sin⁷x] dx

7–64. Integration review Evaluate the following integrals.

60. ∫ from 0 to π/4 of 3√(1 + sin 2x) dx