_0^ /8 ^2 2x 2 ,dx = - Vidyadip

MCQ

$\int_0^{\pi /8} {\frac{{{{\sec }^2}2x}}{2}\,dx = } $

✓
$\frac{1}{4}$
B
$\frac{1}{3}$
C
$\frac{1}{2}$
D
None of these

✓

Answer

Correct option: A.

$\frac{1}{4}$

a
(a) $\frac{1}{2}\int_0^{\pi /8} {{{\sec }^2}2xdx = \frac{1}{4}[\tan 2x]_0^{\pi /8}} $

$= \frac{1}{4}[1] = \frac{1}{4}$.

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

Evaluate: $\int\left(e^{x \log a}+e^{a \log x}+e^{a \log a}\right) d x$

The domain of the derivative of the function $f(x) = \left\{ \begin{array}{l}{\tan ^{ - 1}}x\;\;\;\;\;,\;|x|\; \le 1\\\frac{1}{2}(|x|\; - 1)\;,\;|x|\; > 1\end{array} \right.$ is

If $f'(x) = {x^2} + 5$ and $f(0) = - 1$, then $f(x) = $

The area of the region between the curve $y^2=4 a x$, line $y=2 a$ and $y$-axis is :

The maximum value of Z = 3x + 4y subjected to constraints $\text{x}+\text{y}\leq4,\text{x}\geq0$ and $\text{y}\geq0$ is:

If $\text{A}=\begin{bmatrix}\cos\theta&-\sin\theta\\\sin\theta&\cos\theta\end{bmatrix},$ then $A^T + A = I_2,$ if:

Solution of differential equation $\frac{{dy}}{{dx}} = \frac{{y - x}}{{y + x}}$ is

If $A$ and $B$ are matrices of the same order, then $AB^T - BA^T$ is a:

Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following :
Assertion $ (A) : \frac{\text{d}}{\text{dx}}(\text{x}^2+\text{x}+1)^4=(\text{x}^2+\text{x}+1)^3(2\text{x}+1)$
Reason $ (R) : (\text{fog}\ '=\text{f '}[\text{g(x)}].\text{g '(x)}$

If $\vec{\text{a}}=2\hat{\text{i}}-3\hat{\text{j}}-\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}+4\hat{\text{j}}-2\hat{\text{k}},$ then $\vec{\text{a}}\times\vec{\text{b}}$ is: