A force of Ay2+By+C acts on a body in y direction. The work done by this force during a displacement from y = -a to y = +a will be _________

Question : A force of Ay²+By+C acts on a body in y direction. The work done by this force during a displacement from y = -a to y = +a will be _________

Doubt by Yashika

Solution :

We know,
w = ∫^xf _xi F(y) dy

w = ∫^+a _-a (Ay²+By+C)dy

w = [(Ay³/3) + By²/2  + Cy]^+a_-a
w = [(Ay³/3) + By²/2  + Cy]^+a_-a
w = [{(A(+a)³)/3 + B(+a)2/2 + C(+a)} - {(A(-a)³)/3 + B(-a)2/2 + C(-a)}]
w = [{(Aa³)/3+Ba²/2 +Ca}-{-(Aa³)/3 + Ba²/2 -Ca}]
w = [(Aa³)/3+Ba²/2 +Ca+(Aa³)/3 - Ba²/2 + Ca]
w = (2Aa³)/3 + 2Ca