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G(x) = integral from 1 to x of tan t dt. A) Find G(1). B) Find G prime (pi/6).

Question:

{eq}G(x) = \int_{1}^{x} \tan t \, \mathrm{d}t {/eq}

A) Find {eq}G(1) {/eq}.

B) Find {eq}{G}'(\frac{\pi}{6}) {/eq}.

Fundamental Theorem of Calculus:

According to the fundamental theorem of calculus, if f(x) is a continuous real-valued function defined on a

closed interval (a, b) and F(x) is defined by the integral

{eq}F(x) = \int_{a}^{x} f(t) dt {/eq}

then F(x) is uniformly continuous and differentiable in (a,b) and

{eq}F'(x) = f(x) {/eq}

Answer and Explanation: 1

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We know that the function G(x) is defined by the integral

{eq}G(x) = \int_{1}^{x} \tan t \, \mathrm{d}t {/eq}

a) {eq}G(1) = \int_{1}^{1} \tan t =...

See full answer below.


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The Fundamental Theorem of Calculus

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Chapter 12 / Lesson 10
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The fundamental theorem of calculus links derivatives and antiderivatives in order to find the area under a curve. Learn more about the theorem with an example using velocity.


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