Antidifferentiation — Quiz 4

Questions in this quiz (6)

1. Evaluate $$\int_0^2 \sqrt{4x+5}\,dx$$.

   • $$\frac{(4x+5)^{3/2}}{6}\Big|_2^0$$
   • $$\frac{(4x+5)^{3/2}}{6}\Big|_0^2$$
   • $$\frac{(4x+5)^{1/2}}{6}\Big|_0^2$$
   • $$(4x+5)^{3/2}\Big|_0^2$$

2. Evaluate $$\int \frac{\cos(e^{-x})}{e^x}\,dx$$.

   • $$\sin(e^{-x})+C$$
   • $$\cos(e^{-x})+C$$
   • $$-\sin(e^{-x})+C$$
   • $$-\cos(e^{-x})+C$$

3. Evaluate $$\int \sin^2(4x)\cos(4x)\,dx$$.

   • $$\frac{\sin^3(4x)}{12}+C$$
   • $$\sin^3(4x)+C$$
   • $$\frac{\cos^3(4x)}{12}+C$$
   • $$\frac{\sin^2(4x)}{4}+C$$

4. Evaluate $$\int_{\pi/6}^{\pi/3}\csc x\cot x\,dx$$.

   • $$\csc x\Big|_{\pi/6}^{\pi/3}$$
   • $$-\sec x\Big|_{\pi/6}^{\pi/3}$$
   • $$\tan x\Big|_{\pi/6}^{\pi/3}$$
   • $$-\csc x\Big|_{\pi/6}^{\pi/3}$$

5. Evaluate $$\int e^{\cos 2x}\sin 2x\,dx$$.

   • $$\frac12 e^{\cos 2x}+C$$
   • $$-\frac12 e^{\cos 2x}+C$$
   • $$-e^{\cos 2x}+C$$
   • $$e^{\cos 2x}+C$$

6. Evaluate $$\int \frac{x}{(\ln 2)(x^2+9)}\,dx$$.

   • $$\frac{\ln(x^2+9)}{2\ln 2}+C$$
   • $$\frac{\ln(x^2+9)}{\ln 2}+C$$
   • $$\frac{1}{x^2+9}+C$$
   • $$\ln(x^2+9)+C$$