那么,哪个函数是u(x),哪个函数是v(x)呢? 对比公式,u(x)应该是在微分符号前面的一个函数,而v(x)应该是在微分符号后面的,而xsinx dx这个式子中,有两个函数都在微分符号的前面。 所以,我们要做的第一步,就是把其中的一个函数...
Integral ∫10(x(1−x))ndndnx(logx⋅log(1−x))dx∫01(x(1−x))ndndnx(logx⋅log(1−x))dx 7 Calculating ∫π/20(xsinx)ndx∫0π/2(xsinx)ndx 0 Prove ∫∞0(∏nk=1sin(t/kx)t/kx)dt=π2∫0∞(∏k=1nsin(t/kx)t/kx)dt=...
Given: ∫ sin3x dx. ∫ sin3x dx = ∫ sin2x sin x dx. ∫ sin3x dx = ∫ (1- cos2x) sin x dx Now, substitute cos x = t, hence -sinx dx = dt Therefore, ∫ sin3x dx = -∫ (1-t2) dt =–∫dt + ∫t2dt = -t +(t3/3) + C ...
Prove that limn→∞∫30(√sinxn+x+1)dxn→∞∫03(sinxn+x+1)dx exists and evaluate it 1 How to construct a counterexample to limn→∞∫10fn(x)dx=∫10f(x)dxlimn→∞∫01fn(x)dx=∫01f(x)dx 19 On the integral ∫π0sin(x+sin(x+sin(x+⋯)))dx∫0...
{eq}\displaystyle\int x^n\ dx=\dfrac{x^{n+1}}{n+1}+c\\\ \displaystyle\int sinx\ dx=-cosx+c\\\ \displaystyle\int cosx\ dx=sinx+c\\\ \displaystyle\int \dfrac{1}{x}dx=ln\left | x \right |+c\\\ {/eq} Answer and Expl...
Let y = (sinx)^(e^-x + 4x^3), then dy/dx = (e^-x + 4x^3)(sinx)^(e^-x + 4x^3 -1)cosx a. True b. False f(z) = ln z satisfies Cauchy-Riemann equations in polar form. True or false? Let f(x)>0 . If \int _1^{\infty} f(x)dx conver...
What is the primitive of sinx/cos^2x? Homework Statement ∫e^(-x)(1-tanx)secx dx 2. Attempt at a solution I know ∫e^x(f(x)+f'(x))=e^x f(x) and I intuitively know f(x) could be secx here and therefore f'(x) will be secxtanx but I can't figure out how to reach ...
I've got a function \int e^{-x}sinx dx From what I know, only functions which has one or more products with a finite number of successive differentials can be evaluated using integration by parts. Because for \int v du in our choice of du, we want to cut down on the number of ...
sin(x) = 2t/(1 +t2) cos(x) = (1 –t2) / (1 +t2) dx= 2dt/(1 +t2). This means that the trick can convert an integral containing any rational combination of trig functions into one involving only rational functions, which then can (in principle) be integrated in closed form usin...
sincos2cosxxdxxxxdx du=2xdxv=-cosx u=2x dv=cosxdx du=2dxv=sinx 22 sincos2sin2sinxxdxxxxxxdx 22 sincos2sin2cosxxdxxxxxxC 8.2TrigonometricIntegrals PowersofSineandCosine sincos nm uudusincoscossin nn uuduuudu22 sin1cosuu 1.Ifnisodd,leaveonesinufactoranduse forallotherfactorsofsin. ...