Suppose ∫ (1on top and zero on bottom) f(x) dx=3 and ∫ (3 on top and 0 on bottom) f(x) dx =2

Suppose ∫ (1on top and zero on bottom) f(x) dx=3 and ∫ (3 on top and 0 on bottom) f(x) dx =2 Calculate
(a) ∫ (3 on top and 1 on bottom) f(x)dx
(b) ∫ (1 on top and 3 on bottom) f(x)dx
(c) ∫ (2 on top and 2 on bottom) f(x)dx
(d) ∫ (3 on top and 2 on bottom) 2f(x)dx

Hello,

Just remember that for any real values a, b and c:
∫ (a→c) f(x).dx = ∫ (a→b) f(x).dx   +   ∫ (b→c) f(x).dx
∫ (a→b) f(x).dx = - ∫ (b→a) f(x).dx
∫ (a→a) f(x).dx = 0

Since you have:
∫ (0→1) f(x).dx = 3
∫ (0→3) f(x).dx = 2

∫ (1→3) f(x).dx = ∫ (1→0) f(x).dx   +    ∫ (0→3) f(x).dx
   = -∫ (0→1) f(x).dx   +    ∫ (0→3) f(x).dx
   = -3 + 2
   = -1

∫ (3→1) f(x).dx = -∫ (1→3) f(x).dx
   = -(-1)
   = 1

∫ (2→2) f(x).dx = 0

∫ (2→3) 2.f(x).dx
cannot be calculated from the provided data.

Regards,
Dragon.Jade :-)