Definite Integrals by AI

What is the property of definite integrals that states ∫(a to b) f(x) dx = -∫(b to a) f(x) dx?

Find the area under the curve y = x^2 from x = 0 to x = 2.

What is the property of definite integrals that states ∫(a to b) f(x) dx = ∫(a to c) f(x) dx + ∫(c to b) f(x) dx?

Find the area under the curve y = 3x + 2 from x = 1 to x = 4.

What is the property of definite integrals that states ∫(a to b) f(x) dx = ∫(a to b) g(x) dx + ∫(a to b) h(x) dx?

Find the area under the curve y = sin(x) from x = 0 to x = π.

What is the property of definite integrals that states ∫(a to b) f(x) dx = ∫(a to b) f(g(x))g'(x) dx?

Find the area under the curve y = e^x from x = 0 to x = 1.

What is the property of definite integrals that states ∫(a to b) kf(x) dx = k∫(a to b) f(x) dx?

Find the area under the curve y = 1/x from x = 1 to x = 2.