Evaluate the definite integral $$\int_0^2x^2\ dx$$

The result of the definite integral $$\int_0^2x^2\ dx$$ is $$\frac{8}{3}$$ .

In evaluating $$\int x^3(2+x^3)\ dx$$ , what would be the substitution for 𝑢?

The substitution for 𝑢 is $$2+x^3$$ .

Evaluate: $$\int24^xdx$$

The result of the integral $$\int24^xdx$$ is $$\frac{24^x}{\ln\ 24}+C$$ .

Evaluate $$\int_1^3(2x-1)\ dx$$

The result of the integral $$\int_1^3(2x-1)\ dx$$ is $$6$$ .

What is the purpose of substitution in integration?

Substitution simplifies the integral by changing variables, making it easier to evaluate.

Evaluate $$\int x^n dx$$ where n ≠ -1.

The result is $$\frac{x^{n+1}}{n+1} + C$$ .

What is the integral of a constant c?

The integral of a constant c is $$\int c \, dx = cx + C$$ .

What does $$C$$ represent in integration?

$$C$$ represents the constant of integration, accounting for all possible antiderivatives.

What is the power rule for integration?

The power rule states that $$\int x^n dx = \frac{x^{n+1}}{n+1} + C$$ for n ≠ -1.

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

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

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

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

BasCal Last Flashcard Flashcards

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FLASHCARD QUESTION

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3.

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4.

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Using the Vertical Bar Notation, the Fundamental Theorem of Calculus (FTOC) states that if F is an antiderivative of f, then _____________.

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5.

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6.

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What is the Fundamental Theorem of Calculus?

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7.

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Define an antiderivative.

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