For each integral below

MATHEMATICS · Subjective · CBSE · Mathematics · Integrals · Integrals

Problem

For each integral below, a function is suggested as its antiderivative. In every case decide, with justification, whether the suggestion is correct. If it is not correct, write a correct antiderivative. (a) ∫(2x−7) dx\displaystyle \int (2x-7)\,dx; suggestion: x2−7x+Cx^{2}-7x+C (b) ∫(ex−sec⁡2x) dx\displaystyle \int (e^{x}-\sec^{2}x)\,dx; suggestion: ex−tan⁡x+Ce^{x}-\tan x+C (c) ∫(1x+4x3)dx\displaystyle \int \left(\dfrac{1}{x}+4x^{3}\right)dx; suggestion: ln⁡∣x∣+x4+C\ln|x|+x^{4}+C

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