Question

The First Fundamental Theorem of Calculus can be thought of as a short-cut formula for finding the derivative of accumulation functions. Pick a function f(x) and a number a, and find the derivative of the accumulation function ?_a^x f(x) dx. If a different number is picked for a, does that change the derivative of the accumulation? Why/why not? What changes if the upper limit of integration is x^2 instead of x?

          The First Fundamental Theorem of Calculus can be thought of as a short-cut formula for finding the derivative of accumulation functions.

Pick a function f(x) and a number a, and find the derivative of the accumulation function
?_a^x f(x) dx.

If a different number is picked for a, does that change the derivative of the accumulation?
Why/why not? What changes if the upper limit of integration is x^2 instead of x?

The First Fundamental Theorem of Calculus can be thought of as a short-cut formula for finding the derivative of accumulation functions.

Pick a function f(x) and a number a, and find the derivative of the accumulation function
?a^x f(x) dx.

If a different number is picked for a, does that change the derivative of the accumulation?
Why/why not? What changes if the upper limit of integration is x^2 instead of x?

Added by Mohamed R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Eleni Katirtzoglou

04/14/2022

Step 1

Let's say f(x) = x^2 and a = 0. ** Show more…

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The First Fundamental Theorem of Calculus can be thought of as a short-cut formula for finding the derivative of accumulation functions. Pick a function f(x) and a number a, and find the derivative of the accumulation function ∫ a to x f(x) dx. If a different number is picked for a, does that change the derivative of the accumulation? Why/why not? What changes if the upper limit of integration is x^2 instead of x?