int(3-x) sqrt{4-x} , dx = (Where C is a cons | vedclass

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

Question

(C) Let $I = \int(3-x) \sqrt{4-x} \, dx$. Substitute $u = 4-x$,then $du = -dx$,which means $dx = -du$. Also,$x = 4-u$,so $3-x = 3-(4-u) = u-1$. Substi

Vedclass · Accepted Answer

$\frac{2}{3}(4-x)^{3/2} - \frac{2}{5}(4-x)^{5/2} + C$

Vedclass · Answer

(C) Let $I = \int(3-x) \sqrt{4-x} \, dx$. Substitute $u = 4-x$,then $du = -dx$,which means $dx = -du$. Also,$x = 4-u$,so $3-x = 3-(4-u) = u-1$. Substituting these into the integral: $I = \int (u-1) \sqrt{u} (-du) = \int (1-u) \sqrt{u} \, du$ $I = \int (u^{1/2} - u^{3/2}) \, du$ $I = \frac{u^{3/2}}{3/2} - \frac{u^{5/2}}{5/2} + C$ $I = \frac{2}{3} u^{3/2} - \frac{2}{5} u^{5/2} + C$ Substituting $u = 4-x$ back: $I = \frac{2}{3} (4-x)^{3/2} - \frac{2}{5} (4-x)^{5/2} + C$.

$\int(3-x) \sqrt{4-x} \, dx = $ (Where $C$ is a constant of integration.)

Similar Questions

$\int \cos ^{3} x \cdot e^{\log (\sin x)} d x$ is equal to

If $f(x)$ is an anti-derivative of $g(x)$ and $\int f(x) g(x) (1 + f^2(x)) dx = F(x)$,then $F(x) =$

$\int \frac{(\sin^{-1} x)^{\frac{3}{2}}}{\sqrt{1-x^2}} dx =$

$\int \left( \frac{(x^2+2) a^{(x+\tan^{-1} x)}}{x^2+1} \right) dx = $ . . . . . .

$\int \frac{f(x) g^{\prime}(x)-f^{\prime}(x) g(x)}{f(x) g(x)} \times [\log g(x)-\log f(x)] \, dx$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module