Define the integral $$\frac{d}{dx} igg( \frac{1}{n+1} x^{n+1} igg)$$ .

The integral of $$x^n$$ with respect to x is $$\frac{1}{n+1} x^{n+1} + C$$ , where n is not equal to -1.

Evaluate the integral $$\frac{d}{dx} igg( \frac{1}{3} x^3 igg)$$ .

The integral evaluates to $$x^3 + C$$ .

Evaluate $$\text{If } u = 3x^2 + 5, \text{ then } du = 6x \, dx$$ .

This substitution simplifies the integral to $$\frac{1}{3(5+3x^2)^3} + C$$ .

What is the derivative of $$\frac{1}{n} x^n$$ ?

The derivative is $$x^{n-1}$$ .

What is the integral of $$\frac{1}{x}dx$$ ?

The integral is $$\text{ln}|x| + C$$ .

Evaluate $$\text{If } u = \text{sin}(x), \text{ then } du = \text{cos}(x) \, dx$$ .

This substitution simplifies the integral of $$\text{sin}^5(x) \text{cos}(x)dx$$ .

What is the integral of $$\text{cos}(x)dx$$ ?

The integral is $$\text{sin}(x) + C$$ .

Evaluate $$\text{If } u = 3x^2 + 5, \text{ then } du = 6x \, dx$$ .

This substitution simplifies the integral of $$\frac{6x}{(5 + 3x^2)^4}dx$$ .

What is the integral of $$\text{sin}^3(x) \text{cos}(x)dx$$ ?

The integral evaluates to $$\frac{1}{4}\text{sin}^4(x) + C$$ .

Evaluate $$\text{If } u = \text{sin}(x), \text{ then } du = \text{cos}(x) \, dx$$ .

This substitution simplifies the integral of $$\text{sin}^5(x) \text{cos}(x)dx$$ .

What is the integral of $$\text{sin}(x)dx$$ ?

The integral is $$-\text{cos}(x) + C$$ .

Evaluate $$\text{If } u = 3x^2 + 5, \text{ then } du = 6x \, dx$$ .

This substitution simplifies the integral of $$\frac{6x}{(5 + 3x^2)^4}dx$$ .

Integration With U Substitution

Integration With u-Substitution

Flashcard

•

Mathematics

•

11th Grade

•

Practice Problem

•

Hard

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FLASHCARD QUESTION

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.

FLASHCARD QUESTION

Front

Back

FLASHCARD QUESTION

Front

Back

FLASHCARD QUESTION

Front

How do you choose u in u-substitution?

Back

Choose u to be a function inside another function or a part of the integrand that simplifies the integral when substituted.

FLASHCARD QUESTION

Front

Back

FLASHCARD QUESTION

Front

Back

FLASHCARD QUESTION

Front

Back

This substitution leads to a simpler integral.

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