Antidifferentiation — Quiz 2

Questions in this quiz (10)

1. Find the exact area beneath $$y=x^2+2$$ on $$[0,3]$$.

   • $$17$$
   • $$15$$
   • $$18$$
   • $$21$$

2. Find the area beneath $$\cos x$$ on $$[0,\frac{\pi}{2}]$$.

   • $$0$$
   • $$2$$
   • $$1$$
   • $$\frac{\pi}{2}$$

3. Evaluate $$\frac{d}{dx}\left(\int_1^x \sin t\,dt\right)$$.

   • $$\sin x$$
   • $$\cos x$$
   • $$-\sin x$$
   • $$-\cos x$$

4. Evaluate $$\frac{d}{dh}\left(\int_2^{h^2}(x^3-1)\,dx\right)$$.

   • $$2h(h^6-h^2)$$
   • $$2h((h^2)^3-1)$$
   • $$2h(h^3-1)$$
   • $$2h(h^6-1)$$

5. Evaluate $$\frac{d}{dx}\left(\int_x^{x^2}\sqrt{t+1}\,dt\right)$$.

   • $$\sqrt{x^2+1}-\sqrt{x+1}$$
   • $$2x\sqrt{x^2+1}-\sqrt{x+1}$$
   • $$2x\sqrt{x+1}-\sqrt{x^2+1}$$
   • $$2x\sqrt{x^2+1}+\sqrt{x+1}$$

6. Evaluate $$\int_1^4 x^{1/2}\left(3x^3-\frac{2}{\sqrt{x}}\right)\,dx$$.

   • $$220$$
   • $$240$$
   • $$\frac{1004}{3}$$
   • $$272$$

7. Evaluate $$\int_0^{\pi/3}\tan x(\sec x-\tan x)\,dx$$.

   • $$1-\sqrt3+\frac{\pi}{3}$$
   • $$\sqrt3-1$$
   • $$\frac12$$
   • $$\sqrt3$$

8. Evaluate $$\int_{-2}^{2}|x+1|\,dx$$.

   • $$4$$
   • $$6$$
   • $$7$$
   • $$5$$

9. If $$f(x)$$ is defined by the graph below and consists of a semicircle and numerous line segments, evaluate $$\int_0^{10}f(x)\,dx$$

   • $$-1$$
   • $$2\pi-1$$
   • $$\pi+1$$
   • $$\pi-1$$

10. If $$h(t)$$ is defined by the graph below and $$m(x)=\int_{1/2}^{x}h(t)\,dt,$$ approximate $$m\left(\frac{3}{2}\right).$$

    • $$0$$
    • $$\frac{1}{3}$$
    • $$\frac{1}{2}$$
    • $$1$$