Finding Antiderivatives
In Exercises 1–16, find an antid...

Question

Finding Antiderivatives

In Exercises 1–16, find an antiderivative for each function. Do as many as you can mentally. Check your answers by differentiation.

-(1/3)x⁻⁴ᐟ³

Accepted Answer

Welcome back everyone. Find an anti derivative for the function -4 x to the power of -7 halves. A says 8/5 x 2/5 + c. B 8/5 x to the power of 5 halves plus c. C 8/5 x the power of -5/12 plus c, and D 5/8. X the power of -5 halves plus c. For this problem we want to find the family of an inside derivatives capital F of X. Whose derivative is -4 x, the power of -7.5. Notice that x is raised to a constant which is not equal to -1, so we can apply the power rule. Remember that according to the power rule, if, if we multiply some constant c. By x the power of a and identify the derivative of this function. It is going to be equal to c multiplied by a multiplied by x the power of a minus 1. And this is exactly what we're given. It is equal to -4 x to the power of -7 halves. By analogy, we can begin by identifying the value of a equating the exponents. If A minus 1 is equal to -712. Then A is equal to -75 + 1. Which is equal to -5 halves, and this is how we get the value of a. To get the value of C, we can equate CA. And -4 because that's our. Uh efficient, right? CA is -4, so C is equal to -4 divided by A. Which is -4 divided by -5 halves. And that's 4 multiplied by 2 divided by 5, which is 8/5. Therefore we have shown that the derivative of 8/5. X to the power of -5 halves is equal to. -4 acts the power of -71. Now to get the whole family of anti derivatives, let's remember that the derivative of a constant is 0, so. The derivative of 8/5 x, the power of -5 halves plus c. Will also be equal to -4 x to the power of -7 halve. So now the correct answer for this problem corresponds to the answer to C. Thank you for watching.

Finding AntiderivativesIn Exercises 1–16, find an antiderivative for each function. Do as many as you can mentally. Check your answers by differentiation.-(1/3)x⁻⁴ᐟ³

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Finding Antiderivatives
In Exercises 1–16, find an antiderivative for each function. Do as many as you can mentally. Check your answers by differentiation.
-(1/3)x⁻⁴ᐟ³