Evaluate integral from 0 to x of sin(t^2) with respect to t( (∫ )_0^x(sin)(t^2)dt) 相关知识点: 试题来源: 解析 ( (∫ )_0^x(sin)(t^2)dt) is a special integral. The integral is the Fresnel integralfunction.( S(t)]_0^x)Substitute and simplify.( 0)反馈 收藏 ...
Use the half-angleformula to rewrite ( ((sin))^2(t)) as ( (1-(cos)(2t))2).(∫ (1-(cos)(2t))2dt)Since ( 12) is constant with respect to ( t), move ( 12) out of the integral.( 12∫ 1-(cos)(2t)dt)Split the single integral into multipleintegrals.( 12(∫ 1dt+∫...
{eq}I=\int\sin^{5}2t\cos^{2}2tdt\ 2t=u\ I=\frac{1}{2}\int \sin^4u \cos^2u \sin udu\ =\frac{1}{2}\int(1-\cos^{2}u)^2\cos^2u \sin u du\ \cos...Become a member and unlock all Study Answers Try it risk-free for 30 days Try it risk-free Ask a quest...
Evaluate the following integral. \int \cos^4 x \sin x dx Evaluate the following: d/dx (integral from 0 to 1 of e^(arctan x) dx). Evaluate the following integral: \int \dfrac{-12}{x^2 \sqrt{x^2 + 9 dx. Evaluate the following integral. integral_0^5 3 - t^2 / 5 ...
Answer to: Evaluate the following indefinite integral. Integral of sin^2 t dt. By signing up, you'll get thousands of step-by-step solutions to...
T hen du=2d, s 1/2du=dj . Rewrte using u and du.(3-(2)-( 1/2t^2+C)-1/2fs()u)Simplify.)-(+)-)Siceis constant wit respet to u, move六out of the integral.(+c)-(/n())Simplify.-)((+)-sn)duT he integral of sin(u) with respect to u is-cos(u).(5-()-(5(+...
( t(1/2t-1/4(sin)(2t))-(∫ 1/2tdt+∫ -1/4(sin)(2t)dt)) Since ( 1/2) is constant with respect to ( t), move ( 1/2) out of the integral. ( t(1/2t-1/4(sin)(2t))-(1/2∫ tdt+∫ -1/4(sin)(2t)dt)) By the Power Rule, the integral of ( t) with respect...
The solution of (1)(1) is given by x(ξ)=c1cos(tξ)+c2sin(tξ),where t:=1λ−−√.x(ξ)=c1cos(tξ)+c2sin(tξ),where t:=1λ. Plugging in the second boundary condition into x′(ξ)=c2tcos(tξ)−c1tsin(tξ)x′(ξ)=c2tcos(tξ)−c1tsin...
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| Show 5 more comments This answer is useful 33 Save this answer. Show activity on this post. Here is a sketch of another elementary solution based on a proof in Bromwich's Theory of Infinite Series. Using sin(2k+1)x−sin(2k−1)x=2cos2kxsinx and summing f...