What is the integral of $$\frac{1}{x^2}$$ ?

The integral of $$\frac{1}{x^2}dx$$ is $$-\frac{1}{x} + C$$ .

What is the integral of $$\sin(x)$$ ?

The integral of $$\sin(x)dx$$ is $$-\cos(x) + C$$ .

What is the integral of $$e^x$$ ?

The integral of $$e^x dx$$ is $$e^x + C$$ .

What is the integral of $$\cos(x)$$ ?

The integral of $$\cos(x)dx$$ is $$\sin(x) + C$$ .

What is the purpose of the inverse trigonometric integration?

Inverse trigonometric integration is used to integrate functions that result in inverse trigonometric forms, such as $$\int \frac{1}{\sqrt{1-x^2}}dx = \arcsin(x) + C$$ .

What is the integral of $$\frac{1}{\sqrt{1-x^2}}$$ ?

The integral of $$\frac{1}{\sqrt{1-x^2}}dx$$ is $$\arcsin(x) + C$$ .

What is the integral of $$\frac{1}{1+x^2}$$ ?

The integral of $$\frac{1}{1+x^2}dx$$ is $$\arctan(x) + C$$ .

What is the integral of $$\frac{1}{x^2 + a^2}$$ ?

The integral of $$\frac{1}{x^2 + a^2}dx$$ is $$\frac{1}{a}\arctan(\frac{x}{a}) + C$$ .

What is the method of completing the square?

Completing the square is a technique used to rewrite a quadratic expression in the form $$(x-h)^2 + k$$ , which can simplify integration.

What is the integral of $$\frac{1}{\sqrt{a^2 - x^2}}$$ ?

The integral of $$\frac{1}{\sqrt{a^2 - x^2}}dx$$ is $$\arcsin(\frac{x}{a}) + C$$ .

Techniques of Integration BC Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the integration by parts formula?

Back

2.

FLASHCARD QUESTION

Front

When should you use u-substitution?

Back

Use u-substitution when an integral contains a function and its derivative, allowing for a simpler integration process.

3.

FLASHCARD QUESTION

Front

What is the formula for u-substitution?

Back

4.

FLASHCARD QUESTION

Front

What is the natural log pattern in integration?

Back

5.

FLASHCARD QUESTION

Front

What is the method of partial fractions?

Back

Partial fractions is a technique used to break down a complex rational function into simpler fractions that can be integrated individually.

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

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