Download App

Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
$\int_0^{\pi / 4} \tan ^2 x d x$ is equal to :
  • ✓
    $1-\frac{\pi}{4}$
  • B
    $1+\frac{\pi}{4}$
  • C
    $-1+\frac{\pi}{4}$
  • D
    $-1-\frac{\pi}{4}$
✓

Answer

Correct option: A.
$1-\frac{\pi}{4}$
(A)
$
\begin{aligned}
\int_0^{\pi / 4} \tan ^2 x d x & =\int_0^{\pi / 4}\left(\sec ^2 x-1\right) d x \\
& =\int_0^{\pi / 4} \sec ^2 x d x-\int_0^{\pi / 4} d x \\
& =(\tan x)_0^{\frac{\pi}{4}}-(x)_0^{\frac{\pi}{4}} \\
& =\left(\tan \frac{\pi}{4}-\tan 0\right)-\left(\frac{\pi}{4}-0\right) \\
& =\left(\tan \frac{\pi}{4}-0-\frac{\pi}{4}\right)=1-\frac{\pi}{4}
\end{aligned}
$
Hence option (A) is correct.

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 Integrals→Integrals — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $A$ denote the matrix $\left[\begin{array}{ll}0 & i \\ i & 0\end{array}\right]$, where $i^2=-1$, and let $I$ denote the identity matrix $\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$. Then, $I+A+A^2+\ldots+A^{2010}$ is
→
If the set A contains 7 elements and the set B contains 10 elements, then the number one-one functions from A to B is:
  1. $^{10}\text{C}_7$
  2. $^{10}\text{C}_7\times7!$
  3. $7^{10}$
  4. $10^7$
→
The function $f:R \to R$ defined by $f(x) = {e^x}$ is
→
In a LPP, if the objective function $Z=a x+b y$ has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the same ______ value.
→
The corner point of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20), (60, 0). The objective function is Z = 4x + 3y. Compare the quantity in Column A and Column B.
Column A
Column B
Maximum of Z
325
  1. The quantity in column A is greater.
  2. The quantity in column B is greater.
  3. The two quantities are equal.
  4. The relationship cannot be determined On the basis of the information supplied.
→
If the curve ay + x2 = 7 and x3 = y, cut orthogonally at (1, 1) then the value of a is:
  1. 1
  2. 0
  3. -6
  4. 6
→
Let $\alpha \in R$ be such that the function

$f(x)=\left\{\begin{array}{ll} \frac{\cos ^{-1}\left(1-\{x\}^{2}\right) \sin ^{-1}(1-\{x\})}{\{x\}-\{x\}^{3}}, & x \neq 0 \\ \alpha, & x=0 \end{array}\right.$

is continuous at $x=0,$ where $\{x\}=x-[x],[x]$ is the greatest integer less than or equal to $X$.

Then :

→
If $\text{A}=\begin{bmatrix}\cos\theta&-\sin\theta\\\sin\theta&\cos\theta\end{bmatrix},$ then AT + A = I2, if:
  1. $\theta=\text{n}\pi,\text{n}\in\text{Z}$
  2. $\theta=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
  3. $\theta=2\text{n}\pi+\frac{\pi}{3},\text{n}\in\text{Z}$
  4. $\text{None of these}$
→
If ${I_n} = \int_0^\infty {{e^{ - x}}{x^{n - 1}}dx,} $ then $\int_0^\infty {{e^{ - \lambda x}}{x^{n - 1}}dx = } $
→
The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (25, 20) and (0, 30). Let Z = px + qy, where p, q > 0. Condition on p and q so that the maximum of Z occurs at both the points (25, 20) and (0, 30) is _______.
  1. 5p = 2q
  2. 2p = 5q
  3. p = 2q
  4. q = 3p
→