antiderivative of sin So F x sin x F x sin x is an antiderivative of cos x cos x Therefore every antiderivative of cos x cos x is of the form sin x C sin x C for some constant C C and every function of the form sin x C sin x C is an antiderivative of cos x cos x
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 It is not adding any constant to cos furnishes yet another antiderivative of sin There are in fact infinitely many functions whose derivative is sin To prove that two antiderivatives of a function may only differ by a constant follow this outline suppose a function has antiderivatives F and G
antiderivative of sin
antiderivative of sin
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Antiderivative Of Sin Squared YouTube
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Solved Determine The Following Integrals Integral X Chegg
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We can find the derivatives of sinx and cosx by using the definition of derivative and the limit formulas found earlier The results are d dx sinx cosx and d dx cosx sinx With these two formulas we can determine the derivatives of x t 50 sin t We have to determine x t and then find the time T that obeys x T 25 text Now armed with our table above we know that the antiderivative of sin t is just cos t text We can check this begin align dfrac d dt left cos t right sin t end align
Thus the sentence the antiderivative of cos x cosx is sin x c sinx c is usually stated as the indefinite integral of cos x cosx is sin x c sinx c and this is generally written as int cos x dx sin x c cosx dx sinx c Actually this is bad notation What function has sin x as its derivative Student cos x Because the derivative of cos x is sin x this is an antiderivative of sin x If G x cos x then G x sin x On the other hand if we had instead chosen G x cos
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Antiderivative of sin x Wolfram Alpha Natural Language Math Input Extended Keyboard Examples Upload Random Compute answers using Wolfram s breakthrough technology knowledgebase relied on by millions of students professionals The antiderivative looks like sine and since we know that the derivative of sin x is cos x the rule for the antiderivative is 9 Sine function Select the ninth example showing sine note that you may have to scroll in the example menu box to find the ninth example The antiderivative looks like cosine but upside down and shifted up
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