Download App

STD 12 - 7.2 definite integral — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 7.2 definite integral1 Mark
MCQ
$\int_0^{\pi /2} {\frac{{\sin x\cos x}}{{1 + {{\sin }^4}x}}\,dx = } $
  • A
    $\frac{\pi }{2}$
  • B
    $\frac{\pi }{4}$
  • C
    $\frac{\pi }{6}$
  • ✓
    $\frac{\pi }{8}$
✓

Answer

Correct option: D.
$\frac{\pi }{8}$
d
(d) Put ${\sin ^2}x = t \Rightarrow dt = 2\sin x\cos x\,dx$

Now $\int_0^{\pi /2} {\frac{{\sin x\cos x}}{{1 + {{\sin }^4}x}}dx = \frac{1}{2}\int_0^1 {\frac{1}{{1 + {t^2}}}dt = \frac{1}{2}[{{\tan }^{ - 1}}t]_0^1 = \frac{\pi }{8}} } $.

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 STD 12 - 7.2 definite integral→STD 12 - 7.2 definite integral — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The value of $\sum\limits_{n = 1}^N {{U_n},} $ if ${U_n} = \left| {\,\begin{array}{*{20}{c}}n&1&5\\{{n^2}}&{2N + 1}&{2N + 1}\\{{n^3}}&{3{N^2}}&{3N}\end{array}\,} \right|$ is
→
If A has $3 \times 3$ order square matrix and $| A |=-5$, then $|\operatorname{adj} A |$ is :
→
$\int_{}^{} {\left[ {\frac{1}{{\log x}} - \frac{1}{{{{(\log x)}^2}}}} \right]dx = } $
→
If A is a square matrix, then AA is a:
→
In transportation models designed in linear programming, points of demand is classified as:
→
Let the volume of a parallelopiped whose coterminous edges are given by $\overrightarrow{\mathrm{u}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\lambda \hat{\mathrm{k}}, \overrightarrow{\mathrm{v}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+3 \hat{\mathrm{k}} $ and $\overrightarrow{\mathrm{w}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}$ be $1\; cu.$ unit. If $\theta$ be the angle between the edges $\overrightarrow{\mathrm{u}}$ and $\overrightarrow{\mathrm{w}},$ then $\cos \theta$ can be
→
If $a = 2i + k,\,\,b = i + j + k$ and $c = 4i - 3j + 7k.$ If $d \times b = c \times b$ and $d\,.\,a = 0,$ then $d$ will be
→
The mapping $f : N \rightarrow N$ is given by $f(n) = 1 + n^2, n \in N$ when $N$ is the set of natural numbers is:
→
$\int_{}^{} {\frac{{3\sin x + 2\cos x}}{{3\cos x + 2\sin x}}\;dx = } $
→
Choose the correct answer from the given four options.
Let f : R → R be defined by $\text{f}(\text{x})=\frac{1}{\text{x}}\ \forall\ \text{x}\in\text{R}.$ Then f is:
→