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 Questions" 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

Matrix $\text{A}=\begin{bmatrix}0&2\text{b}&-2\\3&1&3\\3\text{a}&3&-1 \end{bmatrix}$ is given to be symmetric, find values of a and b.

Write the interval for the principal value of function and draw its graph: $\cos ^{-1} x$.

Evaluate:
$\cos\Big\{\sin^{-1}\Big(-\frac{7}{25}\Big)\Big\}$

Write the interval for the principal value of function and draw its graph: $\cot ^{-1} x$

Find the vector equation one of following plane.
2x - y + 2z = 8

Prove that the function $y=\sin ^p \theta \cdot \cos ^q \theta$ has maxima at $\theta=\tan ^{-1}(\sqrt{p / q})$.

Write a value of $\int\sin^3\text{x}\cos\text{x dx}$

Write the equation of the plane parallel to XOY- plane and passing through the point (2, -3, 5).

Evaluate the definite integral $\int\limits_2^3 {\frac{{dx}}{{{x^2} - 1}}} $

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