Question

plzzzzz....... help !!!? ​

Answer 1

AnswEr :—

Given Expression,

$\displaystyle \sf \: l = \int \big( 3 sin(a) - 4 cos(a) \big)da$

The above expression can be rewritten as :

$\displaystyle \sf \: l = \int3 sin(a). da - \int4cos(a).da$

Consider the above expression to be of the form :

$\sf \: l = l_1 - l_2$

Firstly,

$\displaystyle \: \sf \: l_1 = \int3 \: sin(a)da \\ \\ \displaystyle \longrightarrow \: \sf l_1 = \:3 \int \: sin(a).da \\ \\ \longrightarrow \boxed{ \boxed{ \sf \: l_1 = - 3cos(a) + c}}$

Also,

$\displaystyle \sf \: l_2 = \int 4 cos(a).da \\ \\ \longrightarrow \displaystyle \sf l_2= 4 \int cos(a)da \\ \\ \longrightarrow \boxed{\boxed{\sf l_2 = 4sin(a) + c}} \:$

Integral of :

sin x = - cos x + c

cos x = sin x + c

Thus,the integral would be :

$\sf \: \therefore \: , I = - [4sin(a) + 3cos(a)] + C$