2022年2月21日 · Why isn't the antiderivative of $\sin(2x) = \sin^2(x)$? I notice that derivative of $\sin^2(x) = 2\sin(x)\cos(x)$ which is also equal to $\sin(2x)$. Now, according to the …

What is the antiderivative of sin 2 (x)? Solution: The antiderivative of a function is the integral of the function. To integrate ∫ sin 2 (x) dx we will use integration by part. Also, sin 2 (x) = sin x × …

The integral of sin 2x dx is (-cos 2x)/2+C whereas the integration of sin^2x dx is (x/2)-(sin 2x)/4+C. Learn these formulas along with their proofs using the substitution method.

The derivative of sin 2x is 2 cos 2x. Mathematically, it is written as d/dx(sin 2x) = 2 cos 2x (or) (sin 2x)' = 2 cos 2x. What is the Difference Between the Derivative and Anti Derivative of Sin 2x? …

∫ sin 2 x = x/2 - (sin 2x)/4 + C [Since the integral of cos ax = sin ax / a] ☛Note: Here, ∫ cos 2x dx value can be computed using integration by substitution. where, C is the constant of …

$\begingroup$ It's correct to say that the integral of $\sin^2x\cos x$ is $\frac13\sin^3x$. But that doesn't mean that the integral of $\sin^2x$ is $\frac13\sin^3x/\cos x$. That reasoning would …

$\begingroup$ When I said antiderivative of the aforemetioned integral I meant the function F, which its derivative is sin^6(x)*cos^2(x). $\endgroup$ – user65985 Commented Mar 16, 2013 …

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$\begingroup$ @zwim - Beside the familiar identity $1+\cos 2x = 2\cos^2 x$, I guess I familiarized myself with its sister identity $1+\sin 2x=2\cos^2(\frac\pi4-x)$ as well $\endgroup$ – Quanto …

To arrive at the formulas of cos^2x, we will use various trigonometric formulas. The first formula that we will use is sin^2x + cos^2x = 1 (Pythagorean identity). Using this formula, subtract …