AP EAMCET Engineering 22 Sep 2020 Shift 1 Paper

Section: Mathematics

Question : 62 of 160

Marks: +1, -0

\int \sqrt{1+\sin(2x)}

dx=

Solution:

Rewrite using trig identities

= \int \sqrt{(\cos(x)+\sin(x))^2} dx

\sqrt{(\cos(x)+\sin(x))^2} = (\cos(x)+\sin(x)),

assuming

\;(\cos(x)+\sin(x)) \ge 0

= \int \cos(x) + \sin(x) dx

Apply the Sum Rule:

\int (f(x) \pm g(x)) dx = \int f(x) dx \pm \int g(x) dx

= \int \cos(x) dx + \int \sin(x) dx

\int \cos(x) dx = \sin(x)

\int \sin(x) dx = -\cos(x)

= \sin(x) - \cos(x)

Add a constant to the solution

= \sin(x) - \cos(x) + C

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