Download App

Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals2 Marks
Question
Integrate the function $\frac{4 x+1}{\sqrt{2 x^{2}+x-3}}$
✓

Answer

The given Integrand is: 

Let 2x2 + x – 3 =t
$\Rightarrow$ (4x + 1) dx = dt
$\Rightarrow \int \frac{4 x+1}{\sqrt{2 x^{2}+x-3}} d x=\int \frac{1}{\sqrt{t}} d t$ 
$=2 \sqrt{t}+c$ 
= $2 \sqrt{2 x^{2}+x-3}+C$

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 "2 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

Let $\text{f}:\text{R}-\Big\{-\frac{3}{5}\Big\}\rightarrow\ \text{R}$ be a function defined as $\text{f(x)}=\frac{2\text{x}}{5\text{x}+3}.$ Write f-1: Range of $\text{f}\rightarrow\ \text{R}-\Big\{-\frac{3}{5}\Big\}.$
→
If A is a square matrix of order 3 such that |adj A| = 64, find |A|.
→
Find $\big|\vec{\text{a}}-\vec{\text{b}}\big|$ if
$|\vec{\text{a}}|=2,\big|\vec{\text{b}}\big|=5$ and $\vec{\text{a}}.\vec{\text{b}}=8$
→
What is the cosine of the angle with the vector $\sqrt2\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$ makes with y-axis?
→
If $\begin{vmatrix}3\text{x}&7\\-2&4\end{vmatrix}=\begin{vmatrix}8&7\\6&4\end{vmatrix},$ find the value of x.
→
Compute the indicated products:
$\begin{bmatrix}1&-2\\2&3\end{bmatrix}\begin{bmatrix}1&2&3\\-3&2&-1\end{bmatrix}$
→
Find $\int \frac{\text{d}x}{x^{2} + 4x + 8}$
→
Discuss the continuity of the function f defined by f (x) = $\frac{1}{x}, x \neq 0$
→
Evalute the following integrals:
$\int\frac{1}{\text{x}\log\text{x}}\text{dx}$
→
If Cij is the cofactor of the element aij of the matrix $\text{A}=\begin{bmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{bmatrix},$ then write the value of a32C32.
→