Download App

Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
Evaluate the following integral$:\ \int\sec^2\text{xdx:}$
  • A
    $2\tan\text{x+c}$
  • B
    $\tan2\text{x}+\text{c}$
  • ✓
    $\tan\text{x}+\text{c}$
  • D
    None of these
✓

Answer

Correct option: C.
$\tan\text{x}+\text{c}$
We know that. $\frac{\text{d}}{\text{dx}}(\tan\text{x})=\sec^2\text{x}$
$\therefore\text{d }(\tan\text{x})=\sec^2\text{xdx}$
$\Rightarrow\text{I}=\int\sec^2\text{xdx}=\tan\text{x+c}$

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 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

$\cos^{-1}[\cos(2\cot^{-1}(\sqrt2-1))]= ...........$
→
The shortest distance between the lines $\frac{\text{x}-3}{3}=\frac{\text{y}-8}{-1}=\frac{\text{z}-3}{1}$ and, $\frac{\text{x}+3}{-3}=\frac{\text{y}+7}{2}=\frac{\text{z}-6}{4}$ is:
→
Four fair dice are thrown independently $27$ times. Then the expected number of times, at least two dice show up a three or a five, is
→
$\int(\frac{\cos2\theta-1}{\cos2\theta+1})\text{d}\theta=$
→
$\int {(1 + x - {x^{ - 1}}){e^{x + {x^{ - 1}}}}\,\,dx = } $
→
Let $A = \{1, 2, 3\}$ and $B = \{(1, 2), (2, 3), (1, 3)\}$ be a relation on $A.$ Then, $R$ is:
→
The value of integral $\int\limits_{\frac{\pi }{4}}^{\frac{{3\pi }}{4}} {\frac{x}{{1 + \sin x}}} dx$ is
→
The maximum height is reached in $5$ seconds by a stone thrown vertically upwards and moving under the equation  $10s = 10ut -49{t^2}$, where $ s$ is in metre and $t$ is in second. The value of $u$ is ........ $m/\sec $
→
$\int_{ - \pi /2}^{\pi /2} {{{\sin }^2}x{{\cos }^2}x(\sin x + \cos x)\,dx = } $
→
The function $f (x) = sin^4x + cos^4x$ increases if :
→