Indefinite integrals Quiz 1

Question 1

Find the value of the $$\int{\dfrac{\sin x-\cos x}{\left| \sin x-\cos x \right|}}\,dx$$ where $$\dfrac{\pi }{4} < x < \dfrac{3\pi }{8}$$

Accepted Answer

$$x+c$$

Answer

1

Answer

$$x$$

Answer

-1

Question 2

Determine the value of $$\int{\left( 10{{x}^{9}}+{{10}^{x}}\ln 10 \right){{\sec }^{2}}\left( {{x}^{10}}+{{10}^{x}} \right)dx}$$

Accepted Answer

$$	an \left( {{x}^{10}}+{{10}^{x}} ight)+C$$

Answer

$$	an \left( {{x}^{10}}+{{10}^{x}} ight)$$

Answer

$$\cos \left( {{x}^{10}}+{{10}^{x}} \right)+C$$

Answer

$${{	an }^{2}}\left( {{x}^{10}}+{{10}^{x}} ight)+C$$

Question 3

Determine the value of $$\int{\left( 2ax+b \right)\cos \left( a{{x}^{2}}+bx+c \right)dx}$$

Accepted Answer

$$\sin \left( a{{x}^{2}}+bx+c \right)+C$$

Answer

$${{\sin }^{2}}\left( a{{x}^{2}}+bx+c \right)+C$$

Answer

$${{\sec }^{2}}\left( a{{x}^{2}}+bx+c \right)+C$$

Answer

$$\sec \left( a{{x}^{2}}+bx+c \right)+C$$

Question 4

If $$f\left( x \right)=\dfrac{x}{\sqrt[3]{a+bx}}$$and$$\int{f\left( x \right)\,dx}=\dfrac{p}{q{{b}^{2}}}{{\left( a+bx \right)}^{\frac{2}{3}}}\left( 2bx-3a \right)\,$$. Then find the value of $$p+q$$.

Accepted Answer

13

Answer

5

Answer

11

Answer

6

Question 5

If the value of integration $$\int{\dfrac{dx}{{{\left( x+1 \right)}^{\frac{2}{3}}}{{\left( 1-x \right)}^{\frac{4}{3}}}}=k{{\left[ \dfrac{1+x}{1-x} \right]}^{\frac{1}{3}}}+C,}$$ then find $$k$$

Accepted Answer

$$k=\dfrac{3}{2}$$

Answer

$$k=\dfrac{2}{3}$$

Answer

$$k=\dfrac{1}{3}$$

Answer

$$k=\dfrac{1}{2}$$