Integral test Quiz 1

Question 1

Write the simplified form of the integral $$\int{\dfrac{dx}{1-11\operatorname{cosx}}}$$.

Accepted Answer

$$\dfrac{1}{2\sqrt{30}}\left| \dfrac{	an \dfrac{x}{2}-\sqrt{\dfrac{5}{6}}}{	an \dfrac{x}{2}+\sqrt{\dfrac{5}{6}}} ight|+c$$

Answer

$$\dfrac{1}{2\sqrt{30}}\left| \dfrac{	an \dfrac{x}{2}+\sqrt{5}}{	an \dfrac{x}{2}-\sqrt{6}} ight|+c$$

Answer

$$\dfrac{1}{2\sqrt{30}}\left| \dfrac{	an \dfrac{x}{2}+\sqrt{\dfrac{5}{6}}}{	an \dfrac{x}{2}-\sqrt{\dfrac{5}{6}}} ight|+c$$

Answer

$$\dfrac{1}{2\sqrt{30}}\left| \dfrac{	an \dfrac{x}{2}+\sqrt{6}}{	an \dfrac{x}{2}-\sqrt{5}} ight|+c$$

Question 2

Write the value of integral $$\int{\dfrac{\cot (\log x)}{x}}dx$$

Accepted Answer

$$\log \left| sin(\log x) \right|+c$$

Answer

$$\log \left| \cos (\log x) \right|+c$$

Answer

$$\log \left| tan(\log x) \right|+c$$

Answer

$$\log \left| \cot (\log x) \right|+c$$

Question 3

Write the value of $$R$$ in the following equation: $$ \ \int{\dfrac{{{3}^{x}}}{\sqrt{1-{{9}^{x}}}}}dx=R{{\sin }^{-1}}\left( {{3}^{x}} ight)$$

Accepted Answer

$$\dfrac{1}{\log 3}$$

Answer

$$\dfrac{1}{\log 5}$$

Answer

$$\dfrac{1}{\log 4}$$

Answer

$$\dfrac{1}{\log 2}$$

Question 4

If $$y=\int_{1}^{e}{\log m}\,dm$$, then write the value of $$y+5$$.

Accepted Answer

$$6$$

Answer

$$7$$

Answer

$$8$$

Answer

$$9$$

Question 5

Write the value of the integral $$\int\limits_{-\pi /8}^{\pi /8}{\left( {{x}^{3}}+	an 3x+\sin 8x ight)dx}$$

Accepted Answer

$$0$$

Answer

$$-1$$

Answer

$$2$$

Answer

$$1$$