e^ ( - ) d equals : - Vidyadip

MCQ

$\int {} $ $e^{\tan \theta} $ $(\sec \theta - \sin \theta )$ $ d\theta $ equals :

A
$- e^{\tan \theta} \sin \theta + c$
B
$e^{\tan \theta}\sin \theta + c$
C
$e^{\tan \theta } \sec \theta + c$
✓
$e^{\tan \theta} \cos \theta + c$

✓

Answer

Correct option: D.

$e^{\tan \theta} \cos \theta + c$

d
Let $I=\int e^{\tan \theta}(\sec \theta-\sec \theta) d \theta$

Substitute $\tan \theta=t \Rightarrow \sec ^{2} \theta d \theta=d t$

$\therefore I=\int e^{t}(\cos \theta-\tan \theta \sec \theta) d t$

$=\int e^{t}\left(\frac{1}{\sqrt{1+t^{2}}}-t \sqrt{1+t^{2}}\right) d t$

As $\frac{d}{d x}\left(\frac{1}{\sqrt{1+t^{2}}}\right)=t \sqrt{1+t^{2}}$

$\therefore I=e^{t}\left(\frac{1}{\sqrt{1+t^{2}}}\right)=e^{\tan \theta} \cos \theta+c$

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 7.1 inderfinite integral→7.1 inderfinite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

A die is tossed twice. Getting a number greater than $4$ is considered a success. Then the variance of the probability distribution of the number of successes is

The length of the perpendicular drawn from the point $(4,-7,3)$ on the $y$-axis is

A and B draw two cards each, one after another, from a pack of well-shuffled pack of 52 cards. The probability that all the four cards drawn are of the same suit is

$\frac{44}{85\times49}$
$\frac{11}{85\times49}$
$\frac{13\times24}{17\times25\times49}$
None of these.

If the curves y = 2e^x and y = ae^−x intersect orthogonally, then a =

$\frac{1}{2}$
$\frac{-1}{2}$
$2$
$2\text{e}^2$

Which of the following is not a convex set?

{(x, y) ; 2x + 5y ≤ 7}
{(x, y) : x^₂ + y² ≤ 4}
{x : |x| = 5}
{(x, y) : 3x² + 2y² ≤ 6}

The area(in sq. units) of the region bounded by the curves $y = 2^x$ and $y = |x +1|$ in the first quadrant is

If $y = {{\sqrt {{x^2} + 1} + \sqrt {{x^2} - 1} } \over {\sqrt {{x^2} + 1} - \sqrt {{x^2} - 1} }}$, then ${{dy} \over {dx}} = $

Are the points (1, 1), (2, 3) and (8, 11) collinear?

The unit vector perpendicular to both the vectors $i -2j + 3k$ and $i + 2j -k$ is

Consider a quadratic equation $ax^2 + bx + c = 0,$ where $2a + 3b + 6c = 0$ and let $g(x) = a\frac{{{x^3}}}{3} + b\frac{{{x^2}}}{2} + cx.$

Statement $1:$ The quadratic equation has at least one root in the interval $(0, 1).$

Statement $2:$ The Rolle's theorem is applicable to function $g(x)$ on the interval $[0, 1 ].$