Exam 34: Methods of Integration

Integrate by parts: $\int \sin^{3} x d x$

Evaluate the integral using the average ordinate method, the trapezoid rule, or Simpson's rule. Choose ten panels of equal width. Check your answer by integration. $\int_{-\pi}^{\pi} \cos \frac{x}{2} d x$

Integrate: $\int\left(e^{\frac{x}{2}}-\pi\right)^{2} d x$

Integrate by parts: $\int x \cos 2 x d x$

Integrate by parts: $\int \tan^{-1} x d x$

Find the area under the curve: $y=\sin^{2} x \cos x+2 x$ from $x=0$ to $x=\pi$ . Round your answer to three significant digits.

Integrate: $\int \frac{-4 x-8}{2 x^{3}-x^{2}+2 x-1} d x$

Find the area bounded by the curve $y=\frac{2 x-1}{x^{2}+2 x}$ and the x-axis from $x=0.5$ to $x=10$ . Round your answer to three significant digits.

Find the average ordinate for the function in the given interval: $y=5-x^{2}$ from $x=0$ to $x=2$ . Round your answer to three significant digits.

Integrate: $\int \frac{x^{2}+4 x+2}{x^{2}+2} d x$

Integrate: $\int \frac{4 x d x}{\sqrt{1-2 x}}$

Integrate: $\int_{0}^{3} \frac{x^{2}}{\sqrt{x+1}} d x$ . Round your answer to three significant digits.

Find the rms value for the function in the given interval: $y=5 \cos 4 x$ from $x=-\frac{\pi}{4}$ to $x=\frac{\pi}{2}$ . Round your answer to three significant digits.

Integrate: $\int \frac{\sqrt{x}}{1+\sqrt[3]{x}} d x$

Integrate: $\int \frac{x^{2} d x}{\sqrt{x^{2}-16}}$

Integrate: $\int(4 x+2) \cos \left(x^{2}+x\right) d x$

Integrate: $\int \cos 4 y d y$

Integrate: $\int \frac{3 x-2}{x^{2}+3 x+2} d x$

Integrate: $\int \frac{4 x^{3}-8 x^{2}+5}{2 x-1} d x$

Integrate: $\int \frac{8 x d x}{(2 x+1)^{3 / 2}}$