Question

$\red{ \bf \: evaluate \: this \: : }\\ \\ \pink{\leadsto \: }\orange{ \displaystyle \int \bf \:sin (a {x}^{2} - bx) \: \: dx}$
​

Answer 1

Answer:

2π this is the answer for the above question

Step-by-step explanation:

I=∫

−π

π

(cosax−sinbx)

2

dx

=∫

−π

π

(cos

2

ax+sin

2

bx−2cosax.sinbx)dx

=∫

−π

π

(cos

2

ax+sin

2

bx)dx, [ Since cosax.sinbx is odd function ].

=2∫

0

π

(cos

2

ax+sin

2

bx)dx

=∫

0

π

[(1+cos2ax)+(1−cos2bx)]dx

=2.∫

0

π

dx+∫

0

π

(cos2ax−cos2bx)dx

=2π+(

2a

sin2ax

−

2b

sin2bx

)

0

π

=2π