Download App

Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
$\int_1^e \frac{1+\log x}{x} d x=$
  • ✓
    $\frac{3}{2}$
  • B
    $\frac{1}{7}$
  • C
    $\frac{1}{e}$
  • D
    $\frac{2}{3}$
✓

Answer

Correct option: A.
$\frac{3}{2}$
(A)
Put $1+\log x= t \Rightarrow \frac{1}{x} d x= dt$
When $x=1, t =1$ and when $x= e , t =2$
$\therefore \quad \int_1^{ e } \frac{1+\log x}{x} d x=\int_1^2 tdt =\left[\frac{ t ^2}{2}\right]_1^2=\frac{3}{2}$

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 "MCQ" from Definite Integration→Definite Integration — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

The general solution of the differntial equation $\frac{\text{dy}}{\text{dx}}=\frac{\text{y}}{\text{x}}$ is:
→
Let M and N be two $3 \times 3$ non-singular skew-symmetric matrices such that $MN = NM$. If $P ^{ T }$ denotes the transpose of. P , then $M ^2 N^2\left( M ^{ T } N \right)^{-1}\left( MN ^{-1}\right)^{ T }$ is equal to
→
Let A be a square matrix of order 3 whose all entries are 1 and let $I_3$ be the identity matrix of order 3 . Then the matrix $A -3 I _3$ is
→
Three integers are chosen at random from the first $20$ integers. The probability that their product is even is,
→
If a relation $R$ is defined on the set $Z$ of integers as follows: $(a, b) \in R ⇔ a^2 + b^2 = 25$. Then, domain $(R)$ is:
→
The acute angle between the line joining the points $(2,1,-3),(-3,1,7)$ and a line parallel to $\frac{x-1}{3}=\frac{y}{4}=\frac{z+3}{5}$ through the point $(-1,0,4)$ is
→
Let $f (x)$ be a polynomial. Then the second order derivatives of $f(e^x)$ is:
→
If lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-\lambda}{2}=\frac{z}{1}$ intersect each other, then $\lambda=$
→
When the compound statement is true for all its components then the statement is called
→
The general solution of differention eqution of the $e^x dy + (ye^x + 2x)dx = 0$ is:
→