Download App

Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
Evaluate: $\int \sec ^2(7-4 x) d x$
  • A
    $\frac{1}{4} \tan (7-4 x)+C$
  • B
    $\frac{1}{4} \tan (7+4 x)+C$
  • C
    $\frac{-1}{4} \tan (7+4 x)+C$
  • ✓
    $\frac{-1}{4} \tan (7-4 x)+C$
✓

Answer

Correct option: D.
$\frac{-1}{4} \tan (7-4 x)+C$
(d) : Let $I=\int \sec ^2(7-4 x) d x$
Put $7-4 x=t \Rightarrow d x=\frac{-1}{4} d t$
$
\therefore \quad I=\int \frac{\sec ^2 t}{-4} d t \Rightarrow I=\frac{\tan t}{-4}+C=\frac{\tan (7-4 x)}{-4}+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 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

Find value of $x$ in equation $\left[\begin{array}{c}x+y+z \\ x+z \\ y+z\end{array}\right]=\left[\begin{array}{l}9 \\ 5 \\ 7\end{array}\right]$
→
The solution of the differential equation $\frac{d y}{d x}=-\left(\frac{x^2+3 y^2}{3 x^2+y^2}\right), y(1)=0$ is
→
The direction cosine of vector $\hat{i}-2 \hat{j}+3 \hat{k}$ is __________ .
→
If $\begin{bmatrix} 1 & -\tan\theta \\ \tan\theta & 1 \end{bmatrix}\begin{bmatrix} 1 & \tan\theta \\ -\tan\theta & 1 \end{bmatrix}-1=\begin{bmatrix} \text{a} & -\text{b} \\ \text{b} & \text{a} \end{bmatrix},$ then:

  1. $\text{a}=1,\text{b}=1$

  2. $\text{a}=\cos2\theta,\text{b}=\sin2\theta$

  3. $\text{a}=\sin2\theta,\text{b}=\cos2\theta$

  4. None of these.

→
The function $\text{f(x)}=\frac{\text{x}^3+\text{x}^2-16\text{x}+20}{\text{x}-2}$ is not defind for x = 2. in order to make f(x) continuous at x = 2, here f(2) should be defined as:
  1. 0
  2. 1
  3. 2
  4. 3
→
If $p = 7i - 2j + 3k$ and $q = 3i + j + 5k,$ then the magnitude of $p - 2q$ is
→
Differential coefficient of ${{{{\tan }^{ - 1}}x} \over {1 + {{\tan }^{ - 1}}x}}$ w.r.t. ${\tan ^{ - 1}}x$ is
→
If $A =$ $\left[ {\begin{array}{*{20}{c}}0&1&2\\1&2&3\\3&a&1\end{array}} \right]$ ,$A^{-1} =$$\left[ {\begin{array}{*{20}{c}}{1/2}&{ - 1/2}&{1/2}\\{ - 4}&3&c\\{5/2}&{ - 3/2}&{1/2}\end{array}} \right]$, then
→
If $y = {\sqrt x ^{{{\sqrt x }^{\sqrt x ....\infty }}}}$, then ${{dy} \over {dx}} = $
→

In a binomial distribution, the probability of getting success is $\frac{1}{4}$ and standard deviation is 3. Then, its mean is:

  1. 6
  2. 8
  3. 12
  4. 10
→