Need help with integration problem (1 Viewer)

[pi-ka-chew]

so it says:

Sketch y = x^2 and mark the points A(a, a^2), B(-a, a^2), P(a,0) and Q(-a, 0).

a) show that the integral from 0 to a of x^2 dx (sorry, can't insert the sign) = 2/3 (area of triangle OAP)

b) show that the integral from -a to a of x^2 dx = 1/3 (area of rectangle ABQP)

i'm not sure how to do it, as it is only pronumberals i.e a and a^2 that are given.

thanks in advance.

 

[shaon0]

so it says:

Sketch y = x^2 and mark the points A(a, a^2), B(-a, a^2), P(a,0) and Q(-a, 0).

a) show that the integral from 0 to a of x^2 dx (sorry, can't insert the sign) = 2/3 (area of triangle OAP)

b) show that the integral from -a to a of x^2 dx = 1/3 (area of rectangle ABQP)

i'm not sure how to do it, as it is only pronumberals i.e a and a^2 that are given.

thanks in advance.

a) S {for a to 0} x^2 dx =a^3/3
2/3. Area AOP=2/3.1/2.(a^2)(a)
=1/3.a^3
=a^3/3

b) S {for a to -a} x^2 dx =2a^3/3
1/3.Area ABQP=a^2.2a
=2a^3*1/3
=2/3.a^3
=2a^3/3