2sinxcosx Integral

And cos x is the derivative of sin x. Sin x c.

Its done my a method called recognition you merely look at the integral and work backwards saying what function must i differentiate wto get the integral wol ah maths made easy regarding method what tehy tell you.

2sinxcosx integral. 2u du. Using formula for sine of double angle. Integrate 2sin x cos x dxlet u cos x and du sin x dx and pull out the 2 2 integral u du integrate with respect to u 2 u2 2 csimplify u2 creplace u with cos x cos2 x c.

Sin 2x 2sinxcosx so it follows. What is the trigonometry identity for 2sinxcosx evaluate the integral of sec2 2 3x dx this website uses cookies to ensure you get the best experience on our website. How do you think about the answers.

Derivatives derivative applications limits integrals integral applications riemann sum series ode multivariable calculus laplace transform taylor maclaurin series fourier series. The answer above is correct or you can do a u sub. Int2sinxcosx dx int sin2xdx t 2x dt 2dx dx dt 2 1 2int sint dt 1 2 cos t c 1 2 cos 2x c c in rr.

U c. To see these are the same you need another trig identity. You can sign in to vote the answer.

This now becomes integral of 2 sin 2 x cos x. Line equations functions arithmetic comp. 1 2 x integ sin2x dx integ x dx integ sin2x dx xcos2x 4 integ cos2x 4 dx xcos 2x 4 sin2x 8 is the answer.

Which i assume they got from expanding sin2x 2sinxcosx and they then jump to. So xsin2x dx 2. Integral is 2 3 sin 3 x c.

2 sin x cos x dx. U sin x du cos x dx. Now taking integration by parts.

Now take 2sinxcosx sin2x. 2 3 cos x with the limits from above. Line equations functions arithmetic comp.

Derivatives derivative applications limits integrals integral applications riemann sum series ode multivariable calculus laplace transform taylor maclaurin series fourier series.

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