MHT CET 2022 11th August Evening Shift | Indefinite Integration Question 48 | Mathematics

If $$f(x)=\sqrt{\tan x}$$ and $$g(x)=\sin x \cdot \cos x$$ then $$\int \frac{f(x)}{g(x)} \mathrm{d} x$$ is equal to (where $$C$$ is a constant of integration)

$$2 \sqrt{\tan x}+C$$

$$\frac{1}{2} \sqrt{\tan x}+C$$

$$\sqrt{\tan x}+C$$

$$\frac{3}{2} \sqrt{\tan x}+C$$

MHT CET 2022 11th August Evening Shift

MCQ (Single Correct Answer)

-0

$$\int \frac{3 x-2}{(x+1)(x-2)^2} \mathrm{~d} x=$$

(where $$C$$ is a constant of integration)

$$\frac{-5}{9} \log (x+1)+\frac{5}{9} \log (x-2)-\frac{4}{3} \times \frac{1}{(x-2)}+C$$

$$\frac{-5}{9} \log (x+1)+\frac{5}{9} \log (x-2)-\frac{1}{x-2}+C$$

$$\frac{1}{9} \log (x+1)+\frac{5}{9} \log (x-2)-\frac{4}{3} \times \frac{1}{(x-2)}+C$$

$$\frac{-5}{9} \log (x+1)+\frac{1}{9} \log (x-2)-\frac{1}{x-2}+C$$

MHT CET 2022 11th August Evening Shift

MCQ (Single Correct Answer)

-0

$$\int \frac{\sin \frac{5 x}{2}}{\sin \frac{x}{2}} d x=$$

(where $$C$$ is a constant of integration.)

$$x+\sin x+\sin 2 x+C$$

$$x+\sin x+\sin 2 x-C$$

$$x+2 \sin x+2 \sin 2 x+C$$

None of these

MHT CET 2022 11th August Evening Shift

MCQ (Single Correct Answer)

-0

$$\text { If } \int e^{x^2} \cdot x^3 \mathrm{~d} x=e^{x^2} \cdot[f(x)+C]$$ (where $$C$$ is a constant of integration.) and $$f(1)=0$$, then value of $$f(2)$$ will be

$$\frac{-3}{2}$$

$$\frac{-1}{2}$$

$$\frac{3}{2}$$

$$\frac{1}{2}$$

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