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Class XII Maths Exercise 7

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Questions and Answers

What is the antiderivative of $cos 3x$?

$3cos 3x + C$

$\frac{1}{3}cos 3x + C$

$\frac{1}{3}sin 3x + C$ (correct)

$3sin 3x + C$

What is the antiderivative of $sin 2x$?

$2sin 2x + C$

$2cos 2x + C$

$-\frac{1}{2}cos 2x + C$ (correct)

$-\frac{1}{2}sin 2x + C$

What is the antiderivative of $2x$?

$x^2 + 1 + C$

$2x^2 + C$

$x^2 + C$

$x^2 + Cx$ (correct)

What is the antiderivative of $e^{2x}$?

$e^{2x} + C$ Signup and view all the answers

Find the antiderivative of $sin(2x)$.

The antiderivative of $sin(2x)$ is $-rac{1}{2}cos(2x) + C$, where $C$ is the constant of integration. Signup and view all the answers

What is the antiderivative of $3x^2$?

$x^3 + C$ Signup and view all the answers

What is the antiderivative of $cos(3x)$?

The antiderivative of $cos(3x)$ is $rac{1}{3}sin(3x) + C$, where $C$ is the constant of integration. Signup and view all the answers

Determine the antiderivative of $e^{2x}$.

The antiderivative of $e^{2x}$ is $rac{1}{2}e^{2x} + C$, where $C$ is the constant of integration. Signup and view all the answers

What is the antiderivative of $f(x)$?

The antiderivative of $f(x)$ cannot be determined without knowing the function $f(x)$. Therefore, the antiderivative of $f(x)$ cannot be found. Signup and view all the answers

Calculate the antiderivative of $g(x)$.

The antiderivative of $g(x)$ cannot be determined without knowing the function $g(x)$. Therefore, the antiderivative of $g(x)$ cannot be found. Signup and view all the answers

Study Notes

Antiderivatives of Trigonometric Functions

The antiderivative of $cos 3x$ is $(1/3)sin 3x + C$.
The antiderivative of $sin 2x$ is $(-1/2)cos 2x + C$.
The antiderivative of $sin(2x)$ is $(-1/2)cos(2x) + C$.
The antiderivative of $cos(3x)$ is $(1/3)sin(3x) + C$.

Antiderivatives of Algebraic Functions

The antiderivative of $2x$ is $x^2 + C$.
The antiderivative of $3x^2$ is $x^3 + C$.

Antiderivatives of Exponential Functions

The antiderivative of $e^{2x}$ is $(1/2)e^{2x} + C$.

General Antiderivatives

The antiderivative of $f(x)$ is $F(x) + C$, where $F'(x) = f(x)$.
The antiderivative of $g(x)$ is $G(x) + C$, where $G'(x) = g(x)$.

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Description

Test your knowledge of integrals with this Class XII Maths Exercise 7.1 quiz. Practice finding the antiderivatives of sin 2x, cos 3x, and more. Strengthen your understanding of integration techniques and enhance your problem-solving skills.