Integration of Exponential Functions Practice Problems Online

Let $N = \displaystyle \int_0^{7} 4 e^{4 x}\ dx$ . If $N = e^{a} - b$ , where $a$ and $b$ are positive integers, what is the value of $a + b$ ?

If $f(x)$ is a function such that $f(x)=\int e^{x+2} dx$ and $f(-2)=6,$ what is the value of $f(x)?$

If $\displaystyle f(0)=7-\frac{15}{4 \ln 4}$ for the function $f(x)=\int \left( 2 ^x + 2 ^{-x} \right)^2 dx,$ what is the value of $f(1)?$

What is the value of $x$ that satisfies $\sin \left( \frac{\pi}{2} \log_{x^3}\left( \frac{d}{dx}\left( \int x dx \right)\right)\right)=x^2-8x-\frac{65}{2}?$

If $f(x)=\int \frac{27 ^x-64}{3 ^x-4} dx$ and $\displaystyle f(0)=\frac{4}{\ln 3},$ what is the value of $f(1)?$

Concept Quizzes

Challenge Quizzes

Integration of Exponential Functions

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 8 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.