MHT CET 2022 11th August Evening Shift | Indefinite Integration Question 51 | Mathematics

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

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

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

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

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

MHT CET 2021 22th September Evening Shift

MCQ (Single Correct Answer)

-0

$$\int \frac{\tan ^4 \sqrt{x} \cdot \sec ^2 \sqrt{x}}{\sqrt{x}} d x=$$

$$\frac{-5}{2}[\tan \sqrt{x}]^5+c$$

$$[\tan \sqrt{\mathrm{x}}]^5+c$$

$$\frac{2}{5}[\tan \sqrt{x}]^5+c$$

$$\frac{5}{2}[\tan \sqrt{x}]^5+c$$

MHT CET 2021 22th September Evening Shift

MCQ (Single Correct Answer)

-0

$$\int \cos ^{-1} x d x=$$

$$x \cos ^{-1} x+\sqrt{1-x^2}+c$$

$$-x \cos ^{-1} x+\sqrt{1+x^2}+c$$

$$x \cos ^{-1} x-\sqrt{1+x^2}+c$$

$$x \cos ^{-1} x-\sqrt{1-x^2}+c$$

MHT CET 2021 22th September Evening Shift

MCQ (Single Correct Answer)

-0

$$\int \frac{1}{\cos x+\sqrt{3} \sin x} d x=$$

$$2 \log \left[\tan \left(\frac{\mathrm{x}}{2}+\frac{\pi}{12}\right)\right]+\mathrm{c}$$

$$\frac{1}{2} \log \left[\tan \left(\frac{\mathrm{x}}{2}-\frac{\pi}{12}\right)\right]+\mathrm{c}$$

$$\frac{1}{2} \log \left[\tan \left(\frac{\mathrm{x}}{2}+\frac{\pi}{12}\right)\right]+\mathrm{c}$$

$$2 \log \left[\tan \left(\frac{\mathrm{x}}{2}-\frac{\pi}{12}\right)\right]+\mathrm{c}$$

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