10 Questions
What is the antiderivative of $cos 3x$?
$\frac{1}{3}sin 3x + C$
What is the antiderivative of $sin 2x$?
$-\frac{1}{2}cos 2x + C$
What is the antiderivative of $2x$?
$x^2 + Cx$
What is the antiderivative of $e^{2x}$?
$e^{2x} + C$
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.
What is the antiderivative of $3x^2$?
$x^3 + C$
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.
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.
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.
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.
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 $G'(x) = g(x)$.
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.
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