Exam 34: Methods of Integration

Integrate: $\int x^{2} \sin x^{3} d x$

Evaluate the integral using the average ordinate method, the trapezoid rule, or Simpson's rule. Choose ten panels of equal width. Check you answer by integration. $\int_{0}^{\frac{\pi}{4}} \sec^{2} x d x$

Integrate: $\int \tan (1-3 x) d x$

Integrate: $\int x \tan 2 x d x$

Find the average ordinate for the function in the given interval: $y=\frac{x}{\sqrt{x^{2}-15}}$ from 4 to 8

Integrate: $\int x \cot \left(x^{2}+1\right) dx$

Find the volume of the solid generated by rotating the area between $y=\sin x$ and the $x$ -axis from $\mathrm{x}=0$ to $\mathrm{x}=\pi$ about the $\mathrm{x}$ -axis. Round your answer to three significant digits.

Evaluate the improper integral: $\int_{0}^{1} \frac{d x}{x^{2}}$

Integrate by parts: $\int_{0}^{4} 8 x e^{2 x} d x$

Integrate: $\int_{0.1}^{0.5} \frac{d x}{x^{2} \sqrt{1-x^{2}}}$

Integrate by parts: $\int \frac{x^{5} d x}{\sqrt{1-2 x^{3}}}$

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

Integrate: $\int \sqrt{7^{5 x}} d x$

Find the volume generated by rotating the first quadrant area bounded by the set of curves around the $x$ -axis: $y=3 e^{x}$ and $x=1$ . Round your answer to three significant digits.

Find the average ordinate for the function in the given interval: $y=\sqrt{3 x+1}$ from $x=1$ to $x=5$ . Round your answer to three significant digits.

Integrate by parts: $\int_{0}^{\frac{\pi}{2}} 4 x \cos 2 x d x$

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

Evaluate the improper integral: $\int_{1}^{\infty} \frac{2 x d x}{e^{x^{2}}}$ . Round your answer to three significant digits.

Integrate: $\int \frac{4 x^{2}+3 x+9}{x^{3}-9 x} d x$

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