_2^3 x x^2-1 d x - Vidyadip

Question

$\int_2^3 \frac{x}{x^2-1} d x$

✓

Answer

Let $I =\int_2^3 \frac{x}{x^2-1} \cdot d x$
Put $x ^2-1= t$
$
\begin{aligned}
& \therefore 2 x \cdot dx = dt \\
& \therefore x \cdot dx =\frac{1}{2} \cdot d t
\end{aligned}
$
When $x=2, t=2^2-1=3$
When $x=3, t=3^2-1=8$
$
\begin{aligned}
& \therefore I =\int_3^8 \frac{1}{ t } \cdot \frac{ dt }{2} \\
& =\frac{1}{2} \int_3^8 \frac{ dt }{ t } \\
& =\frac{1}{2}[\log | t |]_3^8 \\
& =\frac{1}{2}(\log 8-\log 3) \\
& \therefore I =\frac{1}{2} \log \left(\frac{8}{3}\right) .
\end{aligned}
$

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 Integration (p-1)→Definite Integration (p-1) — all question types→Maths (commerce) STD 12 Commerce / Arts question papers→Maharashtra Board STD 12 Commerce / Arts question papers→Maharashtra Board question paper generator→

Similar questions

Find the Price Index Number using the Simple Aggregate Method.
Use 2000 as the base year in the following problem.

Commodity	Price (in Rs.) for year 2000	Price (in Rs.) for year 2006
Watch	900	1475
Shoes	1800	2300
Sunglasses	600	1040
Mobile	4500	8500

Check whether following matrices are invertible or not: $\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right]$

Given the following data, obtain linear regression estimate of X for Y = 10

What is the present worth of a sum of $\text{₹} 10,920$ due six months hence at $8\%$ p.a simple interest?

Represent the following statements by Venn diagrams : Some non-resident Indians are not rich.

Find $\frac{d y}{d x}$ if $x =5 t ^2, y =10 t$

Using the truth table, prove the following logical equivalences:
p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)

Find $\frac{d y}{d x}$ if, :
$
y=\left(5 x^3-4 x^2-8 x\right)^9
$

In a cattle breeding farm, it is prescribed that the food ratio for one animal must contain 14, 22, and 1 unit of nutrients A, B, and C respectively. Two different kinds of fodder are available. Each unit weight of these two contains the following:

	Fodder 1	Fodder 2
Nutrient A	2	1
Nutrient B	2	3
Nutrient C	1	1

The cost of fodder 1 is ₹ 3 per unit and that of fodder 2 is ₹ 2 per unit. Formulate the LPP to minimize the cost.

Evalute : $\int \frac{x^3}{\sqrt{1+x^4}} d x$