Question

$\int_{-1}^{1} g^{\prime}(x) d x$ is equal to (a) $2 g(-1)$ (b) 0 (c) $-2 g(1)$ (d) $2 g(1)$

Name: Problem 83, Chapter 3: Integral Calculus IIT JEE
Uploaded: 2021-10-22T13:26:45-08:00
Duration: 2 min 48 s
Channel: Srilakshmi E K
Description: ∫-1^1 g^'(x) d x is equal to (a) 2 g(-1) (b) 0 (c) -2 g(1) (d) 2 g(1)

   $\int_{-1}^{1} g^{\prime}(x) d x$ is equal to
(a) $2 g(-1)$
(b) 0
(c) $-2 g(1)$
(d) $2 g(1)$

Integral Calculus IIT JEE

Amit M Agarwal 2018 Edition

Chapter 3, Problem 83

Instant Answer

Solved by Expert Srilakshmi E K

10/22/2021

Step 1

(b) 0: This would be true if $g(1) = g(-1)$. However, we don't have enough information to determine if this is true, so we cannot say this is the correct answer. (c) $-2 g(1)$: This is not equal to $g(1) - g(-1)$, so it's not the correct answer. (d) $2 g(1)$: Show more…

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$\int_{-1}^{1} g^{\prime}(x) d x$ is equal to (a) $2 g(-1)$ (b) 0 (c) $-2 g(1)$ (d) $2 g(1)$

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Key Concepts

Fundamental Theorem of Calculus

This theorem connects the concept of differentiation with integration, stating that if a function is continuous over an interval, then the integral of its derivative over that interval is equal to the difference in the function’s values at the endpoints. It forms the backbone of evaluating definite integrals of derivatives by reducing the problem to finding antiderivatives.

Definite Integral Evaluation

Definite integral evaluation involves computing the accumulated net change of a function between two points. With the fundamental theorem in hand, one substitutes the upper and lower limits into the antiderivative and takes their difference, hence summarizing the overall change in the function over the interval.

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