Evaluate the integral.
-$$\int _ { 2 } ^ { 4 } 3 x \ln x d x$$
A) 20.1
B) 6.70
C) 26.1
D) 4.74

Question

Quizplus · Accepted Answer

Integration by parts: $$u=\ln x, dv=3xdx$$$$du=\frac{1}{x}dx, v=\frac{3x^2}{2}$$$$\int _ { 2 } ^ { 4 } 3 x \ln x d x=\left[\frac{3x^2}{2}\ln x\right]_2^4-\int_2^4\frac{3x^2}{2}\frac{1}{x}dx$$$$=\left[\frac{3(4)^2}{2}\ln 4\right]-\left[\frac{3(2)^2}{2}\ln 2\right]-\int_2^4\frac{3x}{2}dx$$$$=24\ln 4-6\ln 2-\frac{3x^2}{4}\bigg|_2^4$$$$=24\ln 4-6\ln 2-6+3=20.1$$

Evaluate the Integral ∫243xln⁡xdx\int _ { 2 } ^ { 4 } 3 x \ln x d x∫24​3xlnxdx

Evaluate the Integral $\int _ { 2 } ^ { 4 } 3 x \ln x d x$