For example, the integral of {eq}\sin{x} {/eq} is {eq}-\cos{x}+C {/eq}, where {eq}C {/eq} is the integral constant.Answer and Explanation: Given: $$y=\cos\left(2\pi\right) $$ The above expression can be simplified as below: $$\begin{align} y &=\cos\left(2\pi-...
Use integration by parts to find the integral of:[Hint: In (7) write lnx as 1lnx and in (9) write arctanxdn as 1arctanax.](1)xe^x(2)xsinx(3)x^2lnx(4)xsin3x(5)xcos2x(6)xsec^2x(7)lnx(8)(lnx)^2(9)arctanxdn ...
We will use u substitution, and some formula of integrals to evaluate the given integral .Answer and Explanation: ∫cos(x)sin2(x)dx sinx=u=>cosxdx=du Substituting these values ∫duu2 {eq...Become a member and unlock all Study Answers Start today. Try it now Create an...
Again, people memorize that the antiderivative of cosx is sinx. What's the antiderivative of tan? tan x = - ln|cos x| + C. What are the applications of derivatives? Applications of Derivatives in Maths Finding Rate of Change of a Quantity. Finding the Approximation Value. Finding the ...
【题目】Evaluate the definite integral.$$ f _ { \pi / } ^ { \pi } $$m$$ _ { 2 } \frac { \sin x } { 1 + \cos ^ { 2 } x } a $$ 相关知识点: 试题来源: 解析 【解析】 $$ \frac { \pi } { 4 } $$ 结果一 题目 Evaluate the definite integral∫_(-2)^12xdx...
求不定积分Integral of (a*sinx + b*cosx)/(c*sinx + d*cosx) dx(sinx)'=cosx (cosx)'=-sinx,在导数里,是2个非常友好的函数,本题的分子分母结构一样,只是系数不同,可以利用这个条件,用待定系数的方法,将被积函数分解成2个容易积分的函数,求解出答案。, 视频播放量
55. f(x)=sinx,a=0,b=2πf(x)=sinx,a=0,b=2π56. f(x)=cosx,a=0,b=2πf(x)=cosx,a=0,b=2π Show Solution In the following exercises, approximate the average value using Riemann sums L100L100 and R100R100. How does your answer compare with the exact given answer?
Also, we will be using the derivative of the tangent trig function. d(tanx)dx=sec2x Answer and Explanation:1 ∫tan(3x)sec2(3x)etan2(3x)dx. First we will perform ausubstitution. {eq}\displaystyle{ u = \tan^23x\du... ...
Evaluate the integral: \iint_{D}^{}xsinx(x+y)dA, with D={(x,y) 0\leq y\leq \frac{\pi}{3},0\leq x\leq \frac{\pi}{6 Evaluate the integral \int^1_0 \frac{y \ln^4(y^2 + 1)}{y^2 + 1}dy Evaluate the integral of (12)(x^3)(((3x^4) + 4)^4...
2x+3dxAns: 1 10 (2x+3) 5/2 − 1 2 (2x+3) 3/2 +C B−2 Productsofsinesandcosines B39. 2cosxsinxdxAns:sin 2 x+C B40. 2sin3xcos2xdxAns:− 1 5 cos5x−cosx+C B41. 14cos3xcos4xdxAns:sin7x+7sinx+C B42. 8sin3xsinxdxAns:−sin4x+2sin2x+C B43. 4sin 2 xdx...