Download App

Indefinite Integrals — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsIndefinite Integrals2 Marks
Question
Evalute the following integrals:
$\int\frac{1}{\sin\text{x}\cos^2\text{x}}\text{dx}$
✓

Answer

Let $\text{I}=\int\frac{1}{\sin\text{x}\cos^2\text{x}}\text{dx},$ then,
$\text{I}=\int\frac{\sin^2\text{x}+\cos^2\text{x}}{\sin\text{x}\cos^2\text{x}}\text{dx}$
$=\int\frac{\sin^2}{\sin\text{x}\cos^2\text{x}}\text{dx}+\int\frac{\cos^2\text{x}}{\sin\text{x}\cos^2\text{x}}\text{dx}$
$=\int\sec\text{x}\tan\text{x }\text{dx}+\int\text{cosec x dx}$
$=\sec\text{x}+\log\Big|\tan\frac{\text{x}}{2}\Big|+\text{C}$
$\therefore\text{I}=\sec\text{x}+\log\Big|\tan\frac{\text{x}}{2}\Big|+\text{C}$

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

Similar questions

If $y =\tan ^{-1}\left[\frac{\sqrt{1+\cos x}}{1-\cos x}\right]$, find $\frac{ d y}{ d x}$
→
If $\bar{a}=\bar{i}+2 \bar{j}, \bar{b}=-2 \bar{i}+\bar{j}, \bar{c}=4 \bar{i}+3 \bar{j}$, find $x$ and $y$ such that $\bar{c}=x \bar{a}+y \bar{b}$
→
Evaluate the following definite integrals:$\int_{0}^\limits{1}\frac{1}{1+\text{x}^2} \text{ dx}$
→
Find the domain of the following function:$\text{f(x)}=\sin^{-1}\sqrt{\text{x}^2-1}$
→
Find the inverse of matrix $A$ by elementary row transformation, where $A=\left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right]$.
→
Evaluate the following integrals:
$\int\text{e}^{\cos^2\text{x}}\sin2\text{x}\text{ dx}$
→
Evaluate :

$\int_{-a}^a \frac{x+x^3}{16-x^2} \cdot d x$

→
Evaluate the following :

$\int \frac{1}{4 x^2-3} \cdot d x$

→
Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency. (p ∧ q) → (q ∨ p)
→
Let $f: R \rightarrow R^{+}$be defined by $f(x)=a x, a>0$ and $a \neq 1$. Write $f^{-1}(x)$.
→