Given: integral of 3 to 1 f(x) dx is equal to -3 and integral of 3 to 5 f(x)dx is equal to 7, Find: integral of 1 to 5 f(x)dx

Question

Given: integral of 3 to 1 f(x) dx is equal to -3 and integral of 3 to 5 f(x)dx is equal to 7,

Find: integral of 1 to 5 f(x)dx

Answer 1

This question requires that you apply the following two properties of definite integrals:

∫_b^a f(x)dx = - ∫_a^b f(x)dx

∫_a^c f(x)dx = ∫_a^b f(x)dx + ∫_b^c f(x)dx

Try applying the first property to get ∫₁³ f(x)dx, then the second to get ∫₁⁵ f(x)dx.