Definite Integrals Mastery Quiz

What is the antiderivative of $$f(x) = 3x^2$$ ?

According to the Fundamental Theorem of Calculus, if $$F$$ is an antiderivative of $$f$$ on an interval $$[a, b]$$ , what is $$\int_a^b f(x) \, dx$$ ?

Evaluate the definite integral $$\int_0^4 2x \, dx$$ .

What is the area under the curve of $$y = x^2$$ from $$x = 1$$ to $$x = 3$$ ?

Find the antiderivative of $$f(x) = \frac{1}{x}$$ .

Evaluate the definite integral $$\int_{-1}^1 (3x^3 - x) \, dx$$ .

What is the area under the curve of $$y = 4 - x^2$$ from $$x = -2$$ to $$x = 2$$ ?

Find the antiderivative of $$f(x) = e^x$$ .

Evaluate the definite integral $$\int_1^e \frac{1}{x} \, dx$$ .

What is the area under the curve of $$y = \sin(x)$$ from $$x = 0$$ to $$x = \pi$$ ?