Evaluate.
$$ \int_{4}^{5} x\left(x^{2}-16\right)^{3} d x $$
5. (5 points) (a): Evaluate \(\int_{1}^{2} \int_{0}^{2}\left(y+2 x e^{y}\right) d x d y\).(b): Evaluate \(\int_{0}^{1} \int_{0}^{x^{2}} \int_{0}^{x+y}(2 x-y-z) d z d y d x\).
4. Solve the definite integration of the followings:(a) \(\int_{-2}^{2}\left(4 x^{2}-8 x\right) d x\)(b) \(\int_{0}^{2} e^{2 x}-6 x d x\)
4) Evaluate dx (4 – x²) 3/2 5) Evaluate the improper integral ſxe**dx 0 6) Express the repeating decimal 0.123 as a geometric series and then use the sum of that series to express the decimal as the ration of two integers.
Evaluate a) integral 0 to pi (dx/5-4 cos x) b) integral 0 to infinity (dx/(1+x^2)^3)
Question 4 5 pts x2 (A) X Ev Evaluate S 0 - 23azdy + cos,+C X (B) -cos-x+C V1-x2 -cos-x+C -r? + cos2x+c (D) - OD B ОА Question 6 5 pts + Evaluate s da. 6V22 +6 A) 3/72 +6 - 3In XV6 (B) 31n x + 12 +6 + c TV +6 2 (C) 22 +6 - 31n|a + v82 +6|+0 (D) xV22 +6 -2.101x + 4x2 +6|+c 2. 12 ОА D B Oc Question 19 5 pts...
Evaluate the integral. 4) S -2x cos 7x dx Integrate the function. dx (x2+36) 3/2 5) S; 5) Express the integrand as a sum of partial fractions and evaluate the integral. 7x - 10 6) S -dx x² . 44 - 12 6)
14. Evaluate \(\int_{C} y^{3} d x-x^{3} d y, C\) is the circle \(x^{2}+y^{2}=4\) with counterclockwise orientation.
value of z= 96Task 3: Answer the following:a. Evaluate: \(\int_{\frac{\pi}{2}}^{\pi} \boldsymbol{Z} \cos ^{3}(x) \sin ^{2}(x) d x\)b. The moment of inertia, \(I\), of \(a\) rod of mass ' \(m^{\prime}\) and length \(4 r\) is given by \(I=\int_{0}^{4 r}\left(\frac{Z m x^{2}}{2 r}\right) d x\) where \(^{\prime} x^{\prime}\) is the distance from an axis of rotation. Find \(I \)Task 4: Answer the following:Using the Trapezoidal rule, find the approximate the area bounded by the curve\(y=\boldsymbol{Z} e^{\left(\frac{x}{2}\right)}\), the \(\mathrm{x}\) -axis and coordinates \(x=0,...
Evaluate the integral. 3 4 [ rwa f(x) dx where f(x) = 15 - x2 if -3 SXO if 0<x<3
Evaluate \(\int_{C} y^{3} d x-x^{3} d y, C\) is the circle \(x^{2}+y^{2}=4\) with counterclockwise orientation.