Antidifferentiation — Quiz 1

Questions in this quiz (10)

1. Evaluate $$\int\left(\frac45x^4-\frac{3}{x^6}+\sqrt[3]{x^5}\right)\,dx$$.

   • $$\frac{4}{25}x^5-\frac{3}{5x^5}+\frac38x^{8/3}+C$$
   • $$\frac{4}{25}x^5+\frac{3}{5x^5}+\frac38x^{8/3}+C$$
   • $$\frac{4}{25}x^5+\frac{3}{5x^7}+\frac38x^{8/3}+C$$
   • $$\frac45x^5-\frac{3}{5x^5}+\frac83x^{3/8}+C$$

2. Evaluate $$\int cx^d\,dx$$ where $$c$$ and $$d$$ are constants.

   • $$\frac{c}{d}x^d+C$$
   • $$cx^{d+1}+C$$
   • $$\frac{1}{c(d+1)}x^{d+1}+C$$
   • $$\frac{c}{d+1}x^{d+1}+C$$

3. Evaluate $$\int\left(x^{3\pi}+\frac{5}{4x^{1/2}}\right)\,dx$$.

   • $$\frac{x^{3\pi+1}}{3\pi+1}+\frac52x^{1/2}+C$$
   • $$\frac{x^{3\pi}}{3\pi}+\frac52x^{1/2}+C$$
   • $$\frac{x^{3\pi+1}}{3\pi+1}+\frac54x^{1/2}+C$$
   • $$\frac{x^{3\pi+1}}{3\pi+1}+5x^{1/2}+C$$

4. Evaluate $$\int(x^2+2)(x-3)\,dx$$.

   • $$\frac{x^4}{4}-\frac{x^3}{3}-3x^2-6x+C$$
   • $$\frac{x^4}{4}-\frac{x^3}{3}-3x^2+6x+C$$
   • $$\frac{x^4}{4}-x^3+x^2-6x+C$$
   • $$\frac{x^4}{3}-\frac{x^3}{4}-3x^2-6x+C$$

5. Evaluate $$\int\frac{3n^4-2n^2+n-5}{n^2}\,dn$$.

   • $$\frac32n^3-2n+\ln n+\frac5n+C$$
   • $$n^3-2n+\ln n+\frac5n+C$$
   • $$n^3-2n+\ln n-\frac5n+C$$
   • $$n^3-2n-\ln n-\frac5n+C$$

6. Evaluate $$\int\frac{\cos x}{\sin^2 x}\,dx$$.

   • $$\frac{1}{\sin x}+C$$
   • $$\ln(\sin x)+C$$
   • $$\sec x+C$$
   • $$-\frac{1}{\sin x}+C$$

7. Evaluate $$\int(\sec^2 x+2)\,dx$$.

   • $$\tan x+2x+C$$
   • $$\sec x+2x+C$$
   • $$\tan x+x^2+C$$
   • $$\sec^2 x+2x+C$$

8. Evaluate $$\int\frac{x\sqrt{x^2+1}-1}{x\sqrt{x^2+1}}\,dx$$.

   • $$x-\ln|x+\sqrt{x^2+1}|+C$$
   • $$\sqrt{x^2+1}-\ln|x+\sqrt{x^2+1}|+C$$
   • $$x-\ln\left|\frac{x}{1+\sqrt{x^2+1}}\right|+C$$
   • $$\ln|x+\sqrt{x^2+1}|+C$$

9. Approximate the area bounded by $$f(x)=\cos x$$ and the x-axis on the interval $$[0,\frac{\pi}{2}]$$ using $$4$$ rectangles and upper sums.

   • $$0.88$$
   • $$1.18$$
   • $$0.95$$
   • $$0.99$$

10. Use the Trapezoidal Rule to approximate the area beneath the curve $$h(x)=x^2+2$$ on the interval $$[0,3]$$ using (a) $$2$$ subintervals, (b) $$3$$ subintervals, (c) $$4$$ subintervals.

    • $$12.5,\ 12.25,\ 12.17$$
    • $$12.25,\ 12.17,\ 12.12$$
    • $$12.75,\ 12.50,\ 12.25$$
    • $$16.125,\ 15.5,\ 15.28125$$