MHT CET 2024 9th May Evening Shift | Indefinite Integration Question 35 | Mathematics

If $\int \frac{\cos x-\sin x}{\sqrt{8-\sin 2 x}} d x=a \sin ^{-1}\left(\frac{\sin x+\cos x}{b}\right)+c$ Where c is a constant of integration, then the ordered pair $(\mathrm{a}, \mathrm{b})$ is equal to

$(1,3)$

$(3,1)$

$(-1,3)$

$(-3,1)$

MHT CET 2024 9th May Morning Shift

MCQ (Single Correct Answer)

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If $\int \mathrm{f}(x) \mathrm{d} x=\psi(x)$, then $\int x^5 \mathrm{f}\left(x^3\right) \mathrm{d} x$ is equal to

$\frac{1}{3} x^3 \psi\left(x^3\right)-3 \int x^3 \psi\left(x^3\right) \mathrm{d} x+\mathrm{c}$, (where c is a constant of integration)

$\frac{1}{3}\left(x^3 \psi\left(x^3\right)-\int x^3 \psi\left(x^3\right) \mathrm{d} x\right)+\mathrm{c}$, (where c is a constant of integration)

$\frac{1}{3} x^3 \psi\left(x^3\right)-\int x^2 \psi\left(x^3\right) \mathrm{d} x+\mathrm{c}$, (where c is a constant of integration)

$\frac{1}{3}\left(x^3 \psi\left(x^3\right)-\int x^2 \psi\left(x^3\right) \mathrm{d} x\right)+\mathrm{c}$, (where c is a constant of integration)

MHT CET 2024 9th May Morning Shift

MCQ (Single Correct Answer)

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If $\int \frac{d x}{\sqrt[3]{\sin ^{11} x \cos x}}=-\left(\frac{3}{8} f(x)+\frac{3}{2} g(x)\right)+c$ then

$\mathrm{f}(x)=\tan ^{\frac{-8}{3}} x, \mathrm{~g}(x)=\tan ^{\frac{-2}{3}} x$, (where c is a constant of integration)

$\mathrm{f}(x)=\tan ^{\frac{8}{3}} x, \mathrm{~g}(x)=\tan ^{\frac{-2}{3}} x$, (where c is a constant of integration)

$\mathrm{f}(x)=\tan ^{\frac{-8}{3}} x, \mathrm{~g}(x)=\tan ^{\frac{2}{3}} x$, (where c is a constant of integration)

$\mathrm{f}(x)=\tan ^{\frac{8}{3}} x, \mathrm{~g}(x)=\tan ^{\frac{2}{3}} x$, (where c is a constant of integration)

MHT CET 2024 9th May Morning Shift

MCQ (Single Correct Answer)

-0

$\int \frac{x^4+x^2+1}{x^2-x+1} d x$ is equal to

$\frac{x^3}{3}-\frac{x^2}{2}+x+\mathrm{c}$, (where c is a constant of integration)

$\frac{x^3}{3}+\frac{x^2}{2}+x+\mathrm{c}$, (where c is a constant of integration)

$\frac{x^3}{3}-\frac{x^2}{2}-x+\mathrm{c}$, (where c is a constant of integration)

$\frac{x^3}{3}+\frac{x^2}{2}-x+\mathrm{c}$, ( where c is a constant of integration)

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