Antidifferentiation — Quiz 6

Questions in this quiz (5)

1. Set up but do not evaluate $$\int_{-2}^{5}|x^2-3x+2|\,dx$$.

   • Split at roots
   • Split at vertex
   • No split needed
   • Split at endpoints only

2. If $$j(x)=\int_{-2}^{\sin x}\ln(y^2)\,dy$$, find $$j'(x)$$.

   • $$\sin x\cos x$$
   • $$\ln(\sin^2 x)\cos x$$
   • $$\ln x$$
   • $$\cos x$$

3. Which expression has integral $$2\ln|p(2x)|+C$$?

   • $$\frac{2p'(2x)}{p(2x)}$$
   • $$\frac{p'(x)}{p(x)}$$
   • $$2p(2x)$$
   • $$\frac{4p'(2x)}{p(2x)}$$

4. Evaluate $$\int \sec x\,\tan(\ln|\sin x|)\,dx$$.

   • $$\ln|\sin x|+C$$
   • $$\sec x+C$$
   • Source item flawed as written; none of these
   • $$-\cos(\ln|\sin x|)+C$$

5. If $$\int_1^c\left(x^{1/2}-\frac{k}{x}\right)\,dx=7$$, where $$k$$ and $$c$$ are real numbers, find $$k$$ in terms of $$c$$.

   • $$k=\frac{2(c^{3/2}-1)-7}{3\ln c}$$
   • $$k=\frac{\frac{2}{3}(c^{3/2}-1)-7}{\ln c}$$
   • $$k=\frac{7-\frac{2}{3}(c^{3/2}-1)}{\ln c}$$
   • $$k=\frac{2}{3}(c^{3/2}-1)+7$$