Evaluate the definite integral in Exercise: _ 2 ^ 3 1 x dx - Vidyadip

Question

Evaluate the definite integral in Exercise:
$\int_{2}^{3}\frac{1}{\text{x}}\text{dx}$

✓

Answer

$\text{Let} \ \text{I}=\int\limits_{2}^{3}\frac{1}{\text{x}}\ \text{dx}$

$\int\frac{1}{\text{x}}\text{dx}=\text{log}|\text{x|}=\text{F}\text{(x)}$

By second fundamental theorem of calculus, we obtain

$\text{I}=\text{F}(3)-\text{F}(2)$

$=\text{log|3|}-\text{log|2|}=\text{log}\frac{3}{2}$

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

A matrix of order 3 × 3 has determinant 2. What is the value of |A(3I)|, where I is the identity matrix of order 3 × 3.

Evaluate the following integrals:
$\int\limits^{2}_0\text{x}[\text{x}]\text{dx}$

If $\vec{\text{a}}=\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}},\ \vec{\text{b}}=2\hat{\text{i}}-\hat{\text{j}}+3\hat{\text{k}}$and $\vec{\text{c}}=\hat{\text{i}}-2\hat{\text{j}}+\hat{\text{k}}$, find a unit vector parallel to $2\vec{\text{a}}-\vec{\text{b}}+3\vec{\text{c}}$.

Find the magnitude of two vectors $\vec a$ and $\vec b$, having the same magnitude and such that the angle between them is 60^o and their scalar product is $\frac{1}{2}$.

Write the equation of the plane $\vec{\text{r}}=\vec{\text{a}}+\lambda\vec{\text{b}}+\mu\vec{\text{c}}$ in scalar product from.

Verify that the function $y = \sqrt {{a^2} - {x^2}} , $ $x\in \left( { - a,a} \right)$ (explicit or implicit) is a solution of differential equation $x + y\frac{{dy}}{{dx}} = 0\left( {y \ne 0} \right)$

One card is drawn at random from a well shuffled deck of 52 cards. In which of the following cases are the events E and F independent?
E: ‘the card drawn is a king or queen’
F: ‘the card drawn is a queen or jack’

Probability of solving specific problem independently by A and B are $\frac{1}{2}$ and $\frac{1}{3}$ respectively. If both try to solve the problem independently, find the probability that, exactly one of them solve the problem.

For the matrices, A and B, verify that (AB)′ = B′A′, where $A=\left[\begin{array}{l} {0} \\ {1} \\ {2} \end{array}\right], B=\left[\begin{array}{lll} {1} & {5} & {7} \end{array}\right]$

If f : R → R defined by f(x) = 3x - 4 is invertible, then write f^-1(x).