Checking Antiderivative Formulas

Right, or wr...

Question

Checking Antiderivative Formulas

Right, or wrong? Say which for each formula and give a brief reason for each answer.

∫xsinx dx = -x cos x + C

Accepted Answer

Welcome back, everyone. Determine whether the following statement is true or false. The NI derivative of X X is X cosine x plus C. A says true, and B says false. To check if this statement is true or false, what we can do is simply take our inside derivative, find its derivative, and see if it returns the original function x x x. So let's go ahead and find the derivative of X cosine x plus C, where C is a constant. We can distribute the derivative using the properties of differentiation to get X multiplied by cosine x derivative, plus C derivative, right? For the first part, we have the product of two functions. Let's apply the product rule. We get X multiplied by cosine x, plus X multiplied by cosine. of X, right? And then we're adding C. Now, let's find each derivative. The derivative of X is 1. We're multiplying by cosine X, and we're adding X multiplied by cosine x derivative, which is negative sine X. Then the derivative of a constant is 0. Let's go ahead and simplify. This gives us cosine x minus X X X. So we got our derivative, and what we want to do is check if this is equal to X multiplied by sin x. Well, it is not equal to x x x, and because The derivative of the proposed antiderivative is not equal to the original function. We can conclude that the given statement is false and the correct answer is option B. Thank you for watching.

Checking Antiderivative FormulasRight, or wrong? Say which for each formula and give a brief reason for each answer.∫xsinx dx = -x cos x + C

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Checking Antiderivative Formulas

Right, or wrong? Say which for each formula and give a brief reason for each answer.

∫xsinx dx = -x cos x + C