Download App

Definite Integrals — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integrals2 Marks
Question
Evaluate the following integrals:$\int\limits^\frac{\pi}{4}_0\tan\text{x dx}$
✓

Answer

$\int\limits^\frac{\pi}{4}_0\tan\text{x dx}$$=\big[\log\sec\text{x}\big]^{\frac{\pi}{4}}_0$
$=\log\sec\frac{\pi}{4}-\log\sec0$
$=\log\sqrt{2}-\log1$
$=\log2^{\frac{1}{2}}-0$
$=\frac{1}{2}\log2$

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 "Solve the Following Question.(2 Marks)" from Definite Integrals→Definite Integrals — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Transform $\left[\begin{array}{ccc}1 & 2 & 4 \\ 3 & -1 & 5 \\ 2 & 4 & 6\end{array}\right]$ into an upper triangular matrix by using suitable row transformations
→
An urn contains 7 red and 4 blue balls. Two balls are drawn at random with replacement. Find the probability of getting,
One red and one blue ball.
→
Evaluate :

$\int_0^{4 \pi} \frac{\sin 2 x}{\sin ^4 x+\cos ^4 x} \cdot d x$

→
If $R=\left\{(x, y): x^2+y^2 \leq 4 ; x, y \in Z\right\}$ is a relation on $Z$, write the domain of $R$.
→
Solve the following differential equations:
$\frac{\text{dy}}{\text{dx}}=(\cos^2\text{x}-\sin^2\text{x})\cos^2\text{y}$
→
Evaluate the following integrals:$\int^\limits{2\pi}_{0}|\sin\text{x}|\text{dx}$
→
Check whether the following matrix is invertible or not:$
\left[\begin{array}{cc}
\cos \theta & \sin \theta \\
-\sin \theta & \cos \theta
\end{array}\right]
$
→
Let 'o' be a binary operation on the set $Q_0$ of all non-zero rational numbers defined by $\text{a}\ ^*\ \text{b}=\frac{\text{ab}}{2}$ for all $\text{a},\text{b}\in\text{Q}_0.$
Find the invertible elements of $Q_0.$
→
Find the equation of normal to the curve $y=2 x^3-x^2+2$ at $\left(\frac{1}{2}, 2\right)$
→
Find the direction ratios of a vector perpendicular to the two lines whose direction ratios are $1, 3, 2$ and $–1, 1, 2$
→