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.

∫tanθ sec²θ dθ = sec³θ / 3 + C

Accepted Answer

Welcome back everyone. Determine whether the following statement is true or false. The inside derivative of 2 x ln of x 2 is x2 ln x2 minus x2 + c. A says true and B says false. For this problem, what we can do is simply take the derivative of the proposed antiderivative. X2 ln x2 minus x2 + c and check if it returns the original function. What we can do to simplify is differentiate the function and exclude c because the derivative of a constant is 0, so we can just differentiate x 2 ln off x2 minus x2, right? To simplify, we can factor out x2, and this means that we're differentiating x2 in ln of x2 minus 1. Additionally, we can apply the properties of logarithms in particular. The power rule. So that we want to find the derivative of x2 multiplied by 2 ln x minus 1. And we have a product of two functions. So let's apply the product rule, the derivative of x2 multiplied by 2 ln x minus 1, plus x2 multiplied by 2 lnx minus 1 derivative. The derivative of x 2 is 2 x. It is multiplied by 2 ln x minus 1, and we're adding x 2 multiplied by the derivative of ln x is 1 divided by x, so we get 2 divided by x minus the derivative of 1, which is 0, right? Distributing, we get 4 x ln x minus 2 x plus x 2 divided by x gives us x, so we're adding 2 x. And -2 x plus 2x gives us 0. So the derivative is 4 XLN X. We can rewrite it as 2 x multiplied by 2 ln x, which is 2 x multiplied by ln of x squared again using. The power rule we can take our coefficient and write it as as an exponent of x. And this matches the original function given to us in the problem, meaning the statement is true and the answer is a. Thank you for watching.

Checking Antiderivative FormulasRight, or wrong? Say which for each formula and give a brief reason for each answer.∫tanθ sec²θ dθ = sec³θ / 3 + C

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Checking Antiderivative Formulas

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

∫tanθ sec²θ dθ = sec³θ / 3 + C