Question

$\int (1-\frac{x^2}{2!}+\frac{x^4}{4!}-........)dx=$

• A. $sinx+c$
• B. $-sinx+c$
• C. $cosx+c$
• D. $-cosx+c$

Answer 1

Answer: (A)

$sinx+c$

Given,

$1-\frac{x^2}{2!}+\frac{x^4}{4!}-..............$

wkt,

$1-\frac{x^2}{2!}+\frac{x^4}{4!}-..............=\cos x$

the sequence represents a cosine waveform.

Now,

$\int (1-\frac{x^2}{2!}+\frac{x^4}{4!}-............)dx$

$=\int \cos xdx$

$=\sin x+c$