^ - 3/7 x ^ - 11/7 x , ,dx =

MCQ

$\int {{{\cos }^{ - 3/7}}} x{\sin ^{ - 11/7}}x\,\,dx = $

A
$\log |{\sin ^{4/7}}x| + c$
B
$\frac{{ - 7}}{4}{\cot ^{ - 4/7}}x + c$
✓
$\frac{{ - 7}}{4}{\tan ^{ - 4/7}}x + c$
D
(b) and (c) both

✓

Answer

Correct option: C.

$\frac{{ - 7}}{4}{\tan ^{ - 4/7}}x + c$

c
(c) $m + n = - \frac{3}{7} + \left( {\frac{{ - 11}}{7}} \right) = - 2$ (ûve integer)
$I = \int {{{\cos }^{ - 3/7}}x\left( {{{\sin }^{( - 2 + 3/7)}}x} \right)dx} = \int {{{\cos }^{ - 3/7}}} x\,{\sin ^{ - 2}}x\,{\sin ^{3/7}}xdx$
$ = \int {\frac{{\cos e{c^2}x}}{{\left( {\frac{{{{\cos }^{3/7}}x}}{{{{\sin }^{3/7}}x}}} \right)}}} dx = \int {\frac{{\cos e{c^2}x\,dx}}{{{{\cot }^{3/7}}x}}} $
Put $\cot x = t$==> $ - \cos e{c^2}xdx = dt$
$I = - \int {\frac{{dt}}{{{t^{3/7}}}}} $$ = - \frac{{{t^{ - \frac{3}{7} + 1}}}}{{ - \frac{3}{7} + 1}} + c$$ = - \frac{7}{4}{t^{4/7}} + c$
$ = - \frac{7}{4}{\cot ^{4/7}}x + c$$ = - \frac{7}{4}{\tan ^{ - 4/7}}x + c$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 7.1 inderfinite integral→7.1 inderfinite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let X₁ and X₂ are optimal solutions of a LPP, then:

$\text{X}=\lambda\ \text{X}_1+(1-\lambda)\text{X}_2,\lambda\in$ R is also an optimal solution
$\text{X}=\lambda\ \text{X}_1+(1-\lambda)\text{X}_2,0\leq\lambda\leq1$ given an optimal solution
$\text{X}=\lambda\ \text{X}_1+(1+\lambda)\text{X}_2,0\leq\lambda\leq1$ given an optimal solution
$\text{X}=\lambda\ \text{X}_1+(1+\lambda)\text{X}_2,\lambda\in$ R given an optimal solution

→

If $4\,P(A) = 6\,P\,(B) = 10\,P\,(A \cap B) = 1,$ then $P\,\left( {\frac{B}{A}} \right) = $

→

The function $f(x) = e^x + x$, being differentiable and one to one, has a differentiable inverse $f^{-1} (x)$. The value of $(f^{-1})$ at the point $f(l n2)$ is

→

For the set $A=\{1,2,3\}$, define a relation $R$ on the set $A$ as follows :
$R=\{(1,1),(2,2),(3,3),(1,3)\}$
How many ordered pairs to be added to $R$ to make it the smallest equivalence relation?

→

Let $\lambda \in Z, \vec{a}=\lambda \hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=3 \hat{i}-\hat{j}+2 \hat{k}$. Let $\overrightarrow{ c }$ be a vector such that $(\vec{a}+\vec{b}+\vec{c}) \times \vec{c}=\overrightarrow{0}, \vec{a} \cdot \vec{c}=-17$ and $\vec{b} \cdot \vec{c}=-20$ Then $|\overrightarrow{ c } \times(\lambda \hat{i}+\hat{j}+\hat{ k })|^2$ is equal to

→

The set of all real values of $\lambda$ for which the function $f(x)=\left(1-\cos ^{2} x\right) \cdot(\lambda+\sin x)$ $x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right),$ has exactly one maxima and exactly one minima, is

→

$\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)=$