Question
Evaluate the following integrals:$\int_{1}^\limits{3}\frac{\cos(\log\text{x})}{\text{x}}\text{ dx}$
✓
Answer
Let $\text{I}=\int_{1}^\limits{3}\frac{\cos(\log\text{x})}{\text{x}}\text{ dx}$ Let $\log\text{x}=\text{t}$ Then, $\frac{1}{\text{x}}\text{ dx}=\text{dt}$ When $\text{x}=1,\text{t}=0$ and $\text{x}=3,\text{t}=\log3$$\therefore\ \text{I}=\int_{0}^\limits{\log3}\cos\text{t dt}$
$=\big[\sin\text{t}\big]^{\log3}_0$
$=\sin(\log3)$
$=\big[\sin\text{t}\big]^{\log3}_0$
$=\sin(\log3)$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If the matric $\text{A}=\begin{bmatrix}5 & 2&\text{x} \\\text{y} & \text{z}&-3\\4&\text{t}&-7\end{bmatrix}$ is a symmetric matrix, find $x, y, z$ and $t$.
→A coin is biased so that the head is $3$ times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tails.
→Find the expected value, variance, and standard deviation of the random variable whose p.m.f’s are given below:
Evaluate the following integrals:
$\int\text{e}^{\text{x}}(\cot\text{x}+\log\sin\text{x})\text{dx}$
→$\int\text{e}^{\text{x}}(\cot\text{x}+\log\sin\text{x})\text{dx}$
Evaluate the following integrals:
$\int\sin^{-1}\Big(\frac{2\tan\text{x}}{1+\tan^2\text{x}}\Big)\text{dx}$
→$\int\sin^{-1}\Big(\frac{2\tan\text{x}}{1+\tan^2\text{x}}\Big)\text{dx}$
Let $\text{A}=\begin{bmatrix}1&-1&0\\2&1&3\\1&2&1\end{bmatrix}$ and $\text{B}=\begin{bmatrix}1&2&3\\2&1&3\\0&1&1\end{bmatrix},$ Find $A^T, B^T$ and verify that.$(\text{A}+\text{B})^\text{T}=\text{A}^\text{T}+\text{B}^\text{T}$
→Express $\overrightarrow{\text{AB}}$ in terms of unit vectors $\hat{\text{i}}\text{ and }\hat{\text{j}}$, when the point is:A(-6, 3), B(-2, -5)
Find $\Big|\overrightarrow{\text{AB}}\Big|$
→Find $\Big|\overrightarrow{\text{AB}}\Big|$
Determine the value of the constant k so that the function
$\text{f}\text{(x)}=\begin{cases}\frac{\sin2\text{x}}{5\text{x}}, &\text{if}\text{ x}\neq0\\\text{k}, &\text{if}\text{ x}=0\end{cases}$ is continuous at x = 0.
→$\text{f}\text{(x)}=\begin{cases}\frac{\sin2\text{x}}{5\text{x}}, &\text{if}\text{ x}\neq0\\\text{k}, &\text{if}\text{ x}=0\end{cases}$ is continuous at x = 0.
Find the inverse of the following matrices:$\begin{bmatrix}2 & 5 \\ -3 & 1 \end{bmatrix}$
→Integrate the following functions w.r.t x:
→$\frac{\sin x+2 \cos x}{3 \sin x+4 \cos x}$