Evaluate ∫ (4 sin x – 3 cos x) dx.
Answers
EXPLANATION.
⇒ ∫(4Sin x - 3Cos x)dx.
As we know that,
It also write as,
⇒ ∫(4Sin x dx - 3Cos x dx).
⇒ ∫(4Sin x)dx - ∫(3Cos x)dx.
As we know that 4 & 3 are the constant term it take outside from integration, we get.
⇒ 4∫Sin(x)dx - 3∫Cos(x)dx.
⇒ 4(-Cos x) - 3(Sin x) + c.
⇒ -4Cos x - 3Sin x + c.
⇒ -[4Cos x + 3Sin x] + c.
MORE INFORMATION.
Standard integrals.
(1) = ∫Sin(x)dx = -cos(x) + c.
(2) = ∫cos(x)dx = sin(x) + c.
(3) = ∫tan(x)dx = ㏒(sec(x)) + c = -㏒(cos(x)) + c.
(4) = ∫cot(x)dx = ㏒(sin(x)) + c.
(5) = ∫sec(x)dx = ㏒(sec(x) + tan(x)) + c = -㏒(sec(x) - tan(x)) + c = ㏒tan(π/4 + x/2) + c.
(6) = ∫Cosec(x)dx = -㏒(cosec(x) + cot(x)) + c = ㏒(cosec(x) - cot(x)) + c = ㏒tan(x/2) + c.
(7) = ∫sec(x).tan(x)dx = sec(x) + c.
(8) = ∫cosec(x).cot(x)dx = -cosec(x) + c.
(9) = ∫sec²xdx = tan(x) + c.
(10) = ∫cosec²xdx = -cot(x) + c.
Hope it help all.
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