WebDec 14, 2016 · Calculus Introduction to Integration Integrals of Trigonometric Functions 1 Answer sjc Dec 14, 2016 ∫csc2( x 2)dx = − 2cot( x 2) + C Explanation: d dx (cotx) = −csc2x so d dx (cot( x 2)) = − 1 2 csc2x inspecting ∫csc2( x 2)dx we have to adjust for the − 1 2 ∫csc2( x 2)dx = − 2cot( x 2) + C Answer link WebJun 27, 2024 · This proves that the integral of csc^2x is indeed equal to 1. Derivative of csc^2 The derivative of csc^2 is -2*csc*cot. This can be proved by using the power rule and the chain rule. The power rule states that, for any function f (x) = …
How do you integrate int csc^2(x/2) dx? Socratic
WebSolve for x csc(x)=2. Step 1. Take the inverse cosecant of both sides of the equation to extract from inside the cosecant. Step 2. Simplify the right side. Tap for more steps... The … Webintegrate x/(x-1) integrate x sin(x^2) integrate x sqrt(1-sqrt(x)) integrate x/(x+1)^3 from 0 to infinity; integrate 1/(cos(x)+2) from 0 to 2pi; integrate x^2 sin y dx dy, x=0 to 1, y=0 to pi; View more examples » Access instant learning tools. Get immediate feedback and guidance with step-by-step solutions for integrals and Wolfram Problem ... react cookie consent
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Web= [-sin 2 x - cos 2 x] / sin 2 x = - [sin 2 x + cos 2 x] / sin 2 x = -1/sin 2 x --- [Using trigonometric identity sin 2 x + cos 2 x = 1] = -csc 2 x --- [Because sin x = 1/csc x and csc x = 1/sin x] Thus, the derivative of cot x is -csc 2 x. Integral of Cotangent ∫ cot x = ∫ (cos x) / (sin x) dx We will evaluate this integral by substitution method. Websec^2 (x) = 2secx sec^2 (x) = 2secx full pad » Examples Practice Makes Perfect Learning math takes practice, lots of practice. Just like running, it takes practice and dedication. If … WebNov 4, 2024 · To prove the derivative of csc (x) by using first principle, replace f (x) by csc x or replace by csc 2x to calculate derivative of csc2x. f (x)=lim h→0 f (x+h)-f (x)/h f' (x) = lim cosec (x+h) - cosec x/h Since cosec x = 1/sin x, therefore, f' (x) = lim 1/sin (x+h) - 1/sin x/h More simplification, f' (x) = lim sin x - sin (x+h)/hsin x.sin (x+h) how to start car with starter problems