Question

2. Find the value of \( G^{\prime}(1)-G(1) \) where \[ G(x)=\int_{1}^{x^{2}} \sqrt{1+t^{3}} d t \]

          2. Find the value of \( G^{\prime}(1)-G(1) \) where
\[
G(x)=\int_{1}^{x^{2}} \sqrt{1+t^{3}} d t
\]

2. Find the value of G^'(1)-G(1) where

G(x)=∫1^x^2√(1+t^3) d t

Added by Lara R.

Calculus for AP

Jon Rogawski & Ray Cannon 2nd Edition

Chapter 5

Instant Answer

Solved by Expert Jacob Fry

Step 1

We can do this using the chain rule and the Fundamental Theorem of Calculus. Recall that the Fundamental Theorem of Calculus states that if \(F(x) = \int_a^x f(t) dt\), then \(F'(x) = f(x)\). In our case, we have \(G(x) = \int_1^{x^2} \sqrt{1+t^3} dt\), so we Show more…

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