Evaluate the following definite integrals: _ 0 ^1 x x+1 dx - Vidyadip

Question

Evaluate the following definite integrals:
$\int_{0}^\limits{1}\frac{\text{x}}{\text{x}+1}\text{ dx}$

✓

Answer

Let $\text{I}=\int_{0}^\limits{1}\frac{\text{x}}{\text{x}+1}\text{ dx}$ Then,
$\text{I}=\int_{0}^\limits{1}1-\frac{1}{\text{x}+1}\text{ dx}$
$\Rightarrow\text{I}=\big[\text{x}-\log(\text{x}+1)\big]_0^1$
$\Rightarrow\text{I}=1-\log2-(0-\log1)$
$\Rightarrow\text{I}=\log\text{e}-\log2$
$\Rightarrow\text{I}=\log\frac{\text{e}}{2}$

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 Definite Integrals→Definite Integrals — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If on an average 9 ships out of 10 arrive safely at ports, find the mean and S.D. of the ships returning safely out of a total of 500 ships.

Evaluate: $\int\frac{\cos2\text{x}+2\sin^2\text{x}}{\cos^2\text{x}}\text{dx}$

Prove the following Exercise:
$\int^{1}_{0}\text{x e}^{\text{x}}\ \text{dx}=1$

Given an example of two non-zero 2×2 matrices A and B such that AB = 0.

Integrate the function in exercise.
$\text{x} \ \sin\text{x}$

If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9P(X = 3), then find the value of p.

Define a commutative binary operation on a set.

Compute the indicated product
$\left[\begin{array}{cc} {a} & {b} \\ {-b} & {a} \end{array}\right]\left[\begin{array}{cc} {a} & {-b} \\ {b} & {a} \end{array}\right]$

Write the coordinates of the projection of point P(2, -3, 5) on Y-axis.

Find the equation of the plane passing through the following point:
(0, -1, 0), (3, 3, 0) and (1, 1, 1)