Evaluate {eq}\displaystyle \int \sin (2x)\cos (2x) \ dx {/eq} Integration by Substitution: Integration by substitution can be used when one part of our integral is the derivative of the other portion. We recall the substitution rule for integration: If {eq}u=g(x) {/eq} is...
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Sin^2x formulas are used to solve complex integration problems and to prove different trigonometric identities. In the next section, we will derive and explore the formulas of sin square x. Sin^2x Formula To derive the sin2x formula, we will use the trigonometric identities sin2x + cos2x =...
{eq}\int \cos^2 x \sin 2x \, \mathrm{d}x {/eq} Integration by Substitution: Integral by substitution is the method of integration applied to solve an unknown integral. By this method, an unknown integral can be converted into an integral that we know how to solve. The formula of in...
sin2x的不定积分公式：∫xsin2xdx=（-1/2）∫xdcos2x。在微积分中，一个函数f的不定积分，或原函数，或反导数，是一个导数等于f的函数F，即F′=f。不定积分和定积分间的关系由微积分基本定理确定。其中F是f的不定积分。微积分（Calculus），数学概念，是高等数学中研究函数的微分（...
To integrate sin(2x), we use the substitution method. The integral of sin(kx) is given by:∫sin(kx)dx=−1kcos(kx)+CFor our case, k=2:∫sin(2x)dx=−12cos(2x)+C Step 3: Apply the limits of integrationNow we will evaluate the definite integral using the antiderivative we found...
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By integration by parts,∫f(x) . g(x) dx = f(x) ∫g(x) dx − ∫(f′(x) ∫g(x) dx) dx + C∫ sin-1x· 1 dx = sin-1x∫1 dx - ∫ [d/dx(sin-1x) ∫x dx] + C∫ sin-1x dx = sin-1x (x) - ∫ [1/√1 - x²] x dx + C...
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