Mastering Integration Concepts

What is the definition of integration?

• Integration is the process of dividing a function into parts.

• Integration is the graphical representation of a function's slope.

• Integration refers to the sum of all derivatives of a function.

• Integration is the mathematical process of finding the integral of a function.

• 45

• 72

• 63

• 50

State the fundamental theorem of calculus.

• If F is an antiderivative of f on [a, b], then ∫_a^b f(x) dx = F(a) + F(b).

• If F is an antiderivative of f on [a, b], then ∫_a^b f(x) dx = F(b) - F(a).

• If F is a derivative of f on [a, b], then ∫_a^b f(x) dx = F(a) - F(b).

• If F is an antiderivative of f on [a, b], then ∫_a^b f(x) dx = F(b) * F(a).

Choose the correct one

• ∫sin(x) dx = cos(x) + C

• ∫k dx = kx + C

  (k is a constant)

• ∫e^x dx = e^x/x + C

• ∫(x^2 + 1) dx = x/3 + x + C

Evaluate the definite integral ∫(0 to π) sin(x) dx.

• 2

• 2π

• π

• 1

• 15

• 32

• 35

• x + C

• sin(x) + C

• tan^-1(x) + C

• ln(x) + C

What is the relationship between differentiation and integration?

• Differentiation and integration are inverse operations in calculus.

• Differentiation and integration are unrelated concepts.

• Integration is a method to find derivatives.

• Differentiation is the same as integration.