Integration with U Substitution

Front

What is u-substitution in integration?

Back

U-substitution is a method used to simplify the process of integration by substituting a part of the integrand with a new variable (u), making the integral easier to solve.

Front

What is the formula for u-substitution?

Back

Front

Evaluate the integral: ∫5 e^(5x) dx

Back

e^(5x) + C

Front

Evaluate the integral: ∫ 6x (x^2 + 1)^2 dx

Back

(x^2 + 1)^3 + C

Front

What is the derivative of a function?

Back

The derivative of a function measures how the function's output value changes as its input value changes. It is the slope of the tangent line to the function's graph.

Front

Evaluate the derivative: d'(8) if d(t) = 3t^2 - 5t + 2

Back

-3.3 feet per second

Front

Evaluate the definite integral via u-substitution: ∫_0^1 (6x)/(3x^2 + 1)^2 dx

Back

3/4

Front

Evaluate the integral: ∫ 2x cos(x^2) dx

Back

sin(x^2) + C

Front

What is the purpose of definite integrals?

Back

Definite integrals calculate the net area under a curve between two points, providing a numerical value that represents the accumulation of quantities.

Front

What is the Fundamental Theorem of Calculus?

Back