Exam 34: Methods of Integration

Integrate: $\int \frac{d x}{\sqrt{x^{2}-25}}$

Integrate: $\int \frac{2 x^{2}+18 x+20}{x^{3}+4 x^{2}+4 x} d x$

Evaluate: $\int_{1}^{e} \frac{(\ln x)^{2} d x}{x}$

Find the area under one arch of the function: $y=\sin 2 x$

Find the area bounded by the x-axis and the given data points, using any method. Round your answer to three significant digits. 0 1 2 3 4 5 6 7 8 9 10 0.78 1.03 2.54 3.35 4.16 3.84 3.01 3.00 3.39 4.31 5.51

Integrate: $\int_{0}^{2} x e^{x^{2}-1} d x$ . Round your answer to three significant digits.

Integrate: $\int \frac{3 x^{2}-2 x+27}{x^{3}+9 x} d x$

Find the average ordinate for the function $y=\sqrt{4-\frac{x^{2}}{4}}$ in the interval $x=-4$ to $x=4$ .

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

Integrate: $\int \frac{\sin \sqrt{x}}{\sqrt{x}} \cdot d x$

Find the area bounded by the x-axis and the given data points, using any method. Round your answer to three significant digits. 1 3 5 7 9 11 13 15 17 19 21 2.5 2.7 3.2 5.8 6.3 8.1 7.5 5.2 3.8 1.8 0.7

Integrate: $\int e^{x} \sin e^{x} d x$

Integrate: $\int_{1}^{4} \frac{18 x d x}{e^{3 x^{2}}}$

Integrate: Round your answer to three significant digits.

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

Evaluate: $\int_{0}^{\pi / 2} \sin^{4} x \cos x d x$

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

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

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

Evaluate the integral using the average ordinate method, the trapezoid rule, or Simpson's rule. Choose ten panels of equal width. Check you answer by integration. $\int_{0}^{40} \sqrt{x} d x$ . Round your answer to three significant digits.