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Free antiderivative calculator - solve integrals with all the steps. Type in any integral to get the solution, steps and graph.
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The answer is the antiderivative of the function f (x) = sin(x)cos(x) f (x) = sin (x) cos (x). F (x) = F (x) = 1 2sin2 (x)+C 1 2 sin 2 (x) + C. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.
26 Ιουλ 2024 · Suppose the derivative of a function d/dx [f (x)] is F (x) + C then the antiderivative of [F (x) + C] dx of the F (x) + C is f (x). An example explains this if d/dx (sin x) is cos x then, the antiderivative of cos x, given as ∫ (cos x) dx is sin x.
The Integral Calculator lets you calculate integrals and antiderivatives of functions online — for free! Our calculator allows you to check your solutions to calculus exercises. It helps you practice by showing you the full working (step by step integration).
Thus the antiderivative of \cos x cosx is (\sin x) + c (sinx)+ c. The more common name for the antiderivative is the indefinite integral. This is the identical notion, merely a different name for it. A wavy line is used as a symbol for it.
Since we know that the derivative of cos(x) is -sin(x), the derivative of -cos(x) is sin(x), so we would expect that the antiderivative of sine to look like -cosine. The shift comes from the graphing software using the accumulation function so again, the graphed antiderivative must cross the x axis at the origin.
10 Νοε 2020 · \[\dfrac{d}{dx}(\sin x)=\cos x, \nonumber\] so \(F(x)=\sin x\) is an antiderivative of \(\cos x\). Therefore, every antiderivative of \(\cos x\) is of the form \(\sin x+C\) for some constant \(C\) and every function of the form \(\sin x+C\) is an antiderivative of \(\cos x\). d. Since \[\dfrac{d}{dx}(e^x)=e^x, \nonumber\] then \(F(x)=e^x\) is ...
