If an $$anti-derivative$$ of $$f(x)$$ is ex and that of $$g(x)$$ is $$cos$$ x, then ∫$$f(x)$$$$cos$$ ⁡$$xdx+$$∫$$g(x)exdx$$ is equal to

Correct option is 3excos ⁡x+C

Questions

If an anti-derivative of f(x) is e^x and that of g(x) is cos x, then $\int f (x) \cos xdx + \int g (x) e^{x} dx$ is equal to

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f(x)⋅g(x)+C

f(x)+g(x)+C

excos ⁡x+C

f(x)−g(x)+1

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detailed solution

Correct option is C

∫f(x)cos ⁡xdx+∫g(x)exdx=ex2(cos ⁡x+sin⁡ x)−ex2(sin⁡ x−cos⁡ x)+C=ex2(2cos ⁡x)+C=excos ⁡x+C

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If an anti-derivative of f(x) is ex and that of g(x) is cos x, then ∫f(x)cos ⁡xdx+∫g(x)exdx is equal to

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Ready to Test Your Skills?

free study material

If an anti-derivative of f(x) is e^x and that of g(x) is cos x, then $\int f (x) \cos xdx + \int g (x) e^{x} dx$ is equal to