int_{2}^{3} frac{dx}{x^2 - x} = | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $I = \int_{2}^{3} \frac{dx}{x(x - 1)}$.Using partial fractions,we can write $\frac{1}{x(x - 1)} = \frac{1}{x - 1} - \frac{1}{x}$.Therefore,$I

Vedclass · Accepted Answer

$\log(4/3)$

Vedclass · Answer

(C) Let $I = \int_{2}^{3} \frac{dx}{x(x - 1)}$.Using partial fractions,we can write $\frac{1}{x(x - 1)} = \frac{1}{x - 1} - \frac{1}{x}$.Therefore,$I = \int_{2}^{3} \left( \frac{1}{x - 1} - \frac{1}{x} \right) dx$.Integrating term by term,we get $I = [\log|x - 1| - \log|x|]_{2}^{3}$.Using the property $\log a - \log b = \log(a/b)$,we have $I = [\log|\frac{x - 1}{x}|]_{2}^{3}$.Substituting the limits: $I = \log|\frac{3 - 1}{3}| - \log|\frac{2 - 1}{2}|$.$I = \log(2/3) - \log(1/2) = \log(\frac{2/3}{1/2}) = \log(4/3)$.

$\int_{2}^{3} \frac{dx}{x^2 - x} = $

Similar Questions

$\int_0^4 ||x-2|-x| dx = $

Let $\lim _{c \rightarrow 0} \int_c^x \frac{b t \cos 4 t - a \sin 4 t}{t^2} d t = \frac{a \sin 4 x}{x} - 1$. Find the values of $a$ and $b$.

$\int_{\pi / 6}^{\pi / 3} \cos^{-4} x \, dx =$

If $f(x) = \begin{cases} e^{\cos x} \sin x, & \text{for } |x| \leq 2 \\ 2, & \text{otherwise} \end{cases}$,then $\int_{-2}^{3} f(x) dx$ is equal to

$ \int_{0}^{2} [x^{2}] \, dx $

Vedclass Test Series

Exam Paper Generator

Online Exam Module