∫e1 (lnx)2/x dx
$$ \int_{1}^{e} \frac{(\ln x)^{2}}{x} d x $$
Homework Answers
Find the Fourier integral representation of f(x) = e −|x| and hence show that
(15 marks) Find the Fourier integral representation of \(f(x)=e^{-|x|}\) and hence show that$$ \int_{0}^{\infty} \frac{d t}{1+t^{2}}=\frac{\pi}{2} $$
The integral int_{a}^{b} \frac{dx}{(x - a)"p} diverges if . Select one: a. 2p \le 1 b....
The integral int_{a}^{b} \frac{dx}{(x - a)"p} diverges if . Select one: a. 2p \le 1 b. p\ge 1 c. p> 1 d. p < 1
Evaluate integral
Problem 6. ( 25 points) Let \(a, b\) be positive constants with \(a<b\). Evaluate the integral$$ \int_{0}^{1} \frac{x^{b}-x^{a}}{\ln x} d x $$by converting the integral into an iterated double integral and evaluating the iterated integral by changing the order of integration.
Solve the following differential equations x2d2y/dx2 − xdy/dx − 3y = lnx/ x , x >...
Solve the following differential equations x2d2y/dx2 − xdy/dx − 3y = lnx/ x , x > 0. show that the answer is y = A/x + Bx3 − lnx/ 6x (2lnx + 1) x d2y/dx2 − dy/dx + 2y/x = (ln x)2 .show that the answer is y = x { A cos(ln x) + B sin(ln x) + (lnx) 2 − 2 }
Math assignment about extreme of function and mean value theorem due tomorrow
The math assignment was due tomorrow so I need the answers with steps as soon as possible and I need it around today so please hurry1. (15 marks) Find the domain of \(f(x)=2 x-\frac{1}{x^{2}}\) and find the intervals on which the function is increasing or decreasing.2. (15 marks) For \(f(x)=\frac{x^{3}}{x+1}\), find the local maximum and minimum.3. (15 marks) Find the absolute maximum and minimum of the function \(f(x)=\frac{x}{1+x^{2}}\) on the closed interval \([-1,2]\).4. (20 marks) Sketch the graph of the...
Exact answer/fraction
Evaluate \(\int_{C} \mathrm{~F} \cdot d \mathbf{r}\) using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results.$$ \int_{C}[4(2 x+7 y) \mathbf{i}+14(2 x+7 y) \mathbf{j}] \cdot d \mathbf{r} $$C: smooth curve from \((-7,2)\) to \((3,2)\)Evaluate \(\int_{C} \mathrm{~F} \cdot d \mathbf{r}\) using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results.$$ \int_{C} \cos (x) \sin (y) d x+\sin (x) \cos (y) d y $$C: line segment from \((0,-\pi)\) to \(\left(\frac{3 \pi}{2},...
value of z= 96 Task 3: Answer the following
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,...
Prove
Prove:$$ \int_{0}^{1} e^{x} \sqrt{2 x+1}\left(1+x+x^{2}\right)^{100} d x \leq \sqrt{\frac{\left(e^{2}-1\right)\left(3^{201}-1\right)}{402}} $$You may not use any integral computation tools such as Wolfram Alpha for this question. HINT: Think about inner products.
4. Solve the definite integration of the followings: (a) (4x2 – 8x) dx (5 marks) (b)...
4. Solve the definite integration of the followings:(a) \(\int_{-2}^{2}\left(4 x^{2}-8 x\right) d x\)(b) \(\int_{0}^{2} e^{2 x}-6 x d x\)
Evaluate. 5 Sx(x2 - 16) 3 dx 4 5 [x(x2 - 16) º dx=0 (Type an...
Evaluate.$$ \int_{4}^{5} x\left(x^{2}-16\right)^{3} d x $$
The integral int_{a}^{b} \frac{dx}{(x - a)"p} diverges if . Select one: a. 2p \le 1 b. p\ge 1 c. p> 1 d. p < 1
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,...
Prove:$$ \int_{0}^{1} e^{x} \sqrt{2 x+1}\left(1+x+x^{2}\right)^{100} d x \leq \sqrt{\frac{\left(e^{2}-1\right)\left(3^{201}-1\right)}{402}} $$You may not use any integral computation tools such as Wolfram Alpha for this question. HINT: Think about inner products.
Evaluate.$$ \int_{4}^{5} x\left(x^{2}-16\right)^{3} d x $$
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