Definite Integrals — Quiz 1

Questions in this quiz (10)

1. $$\int_0^1\frac{x}{\sqrt{9-x^2}}dx=$$?

   • $$-1$$
   • $$2+\sqrt{2}$$$
   • $$3-2\sqrt{2}$$
   • $$\frac{\sqrt{2}}{2}$$

2. $$\int_1^4\frac{3+x}{3\sqrt{x}}dx=$$?

   • $$\frac{19}{3}$$
   • $$\frac{17}{3}$$
   • $$\frac{32}{9}$$
   • $$\frac{25}{3}$$

3. $$\int_{-1}^{1}\sqrt{2u+5}\,du=$$?

   • $$\sqrt{3}$$
   • $$7\sqrt{7}$$
   • $$\frac{\sqrt{7}}{3}$$
   • $$\frac{1}{3}\left(7\sqrt{7}-3\sqrt{3}\right)$$

4. $$\int_0^1e^{2x}dx=$$?

   • $$\frac{e^2-1}{2}$$
   • $$e^2-1$$
   • $$\frac{e^2}{2}-1$$
   • $$\frac{1}{2}(e^2-1)$$

5. $$\int_1^e\frac{\ln x}{x}dx=$$?

   • $$\frac{1}{2}$$
   • $$1$$
   • $$\frac{1}{2}(e-1)$$
   • $$\ln e$$

6. $$\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\frac{\cos x}{\sin^2 x}dx=$$?

   • $$1$$
   • $$\frac{1}{\sqrt{2}}$$
   • $$-\frac{1}{2}$$
   • $$-\frac{2}{\sqrt{3}}+2$$

7. If we let $$x=3\sin\theta$$ then$$\int_{\frac{3}{2}}^{3}\frac{\sqrt{9-x^2}}{x}dx$$ is equivalent to:

   • $$3\int_{\frac{\pi}{6}}^{\frac{\pi}{2}}\frac{\cos^2\theta}{\sin\theta}d\theta$$
   • $$\int_{\frac{\pi}{6}}^{\frac{\pi}{2}}\frac{\cos\theta}{\sin\theta}d\theta$$
   • $$3\int_{1}^{3}\frac{\cos^2\theta}{\sin\theta}d\theta$$
   • $$\int_{\frac{\pi}{6}}^{\frac{\pi}{2}}\frac{\cos^2\theta}{\sin^2\theta}d\theta$$

8. If we let $$x=\tan\theta$$, then$$\int_1^{\sqrt{3}}(1+x^2)dx$$ is equivalent to:

   • $$\int_{\frac{\pi}{4}}^{\frac{\pi}{3}}\sec^2\theta d\theta$$
   • $$\int_1^{\sqrt{3}}\sec^2\theta d\theta$$
   • $$\int_{\frac{\pi}{4}}^{\frac{\pi}{3}}\sec\theta d\theta$$
   • $$\int_{\frac{\pi}{4}}^{\frac{\pi}{3}}\sec^3\theta d\theta$$

9. The table below shows some values of a continuous function $$f$$ and its first derivative.Evaluate $$\int_{9}^{1}f'(x)dx$$

   • $$-2$$
   • $$2$$
   • $$-4$$
   • $$4$$

10. The graph of a continuous function $$f$$ passes through the points $$(2,3),(5,7),(7,6),(9,10)$$ Using trapezoids, estimate $$\int_2^9f(x)dx$$.

    • $$38$$
    • $$40$$
    • $$44$$
    • $$50$$