Integrating exponentials and trigonometric functions Quiz

1. Find $\int\left(4e^{2x}+\frac1x\right)dx$.

• A. $2e^{2x}+\ln|x|+c$
• B. $8e^{2x}+\ln|x|+c$
• C. $4e^{2x}-\ln|x|+c$
• D. $2e^{2x}+x^{0}+c$

2. Find $\int3\sin4x\,dx$.

• A. $\frac34\cos4x+c$
• B. $-12\cos4x+c$
• C. $-\frac34\cos4x+c$
• D. $\frac34\sin4x+c$

3. Evaluate $\int_0^{\pi/2}\cos 2x\,dx$.

• A. $1$
• B. $0$
• C. $\frac12$
• D. $-1$

4. Evaluate $\int_1^3\frac2x\,dx$.

• A. $\ln6$
• B. $\frac{2}{3}$
• C. $2\ln2$
• D. $2\ln3$

5. A curve has $\frac{dy}{dx}=e^{-x}$ and passes through $(0,3)$. Find $y$.

• A. $y=4-e^{-x}$
• B. $y=e^{-x}+2$
• C. $y=-e^{-x}+3$
• D. $y=e^{-x}+3$