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How do you find the antiderivative of this equation #e^(3x) - 4 cos x#?

Answer 1

Scarlett Allison

In this manner:

#int(e^(3x)-4cosx)dx=1/3int3e^(3x)dx-4intcosxdx=#

#=1/3e^(3x)-4sinx+c#.

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Answer 2

Cameron Alexander

To find the antiderivative of the equation ( e^{3x} - 4 \cos(x) ), you integrate each term separately:

For ( e^{3x} ), the antiderivative is ( \frac{1}{3} e^{3x} + C ).

For ( -4 \cos(x) ), the antiderivative is ( -4 \sin(x) + C ).

So, the antiderivative of the given equation is:

[ \frac{1}{3} e^{3x} - 4 \sin(x) + C ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.