Combining Definite Integrals on Adjacent Intervals
Read this topicExplanations 1
- There is a special property concerning the combination of definite integrals with the same integrand. Generically, it is as follows: ∫abf(x)dx+∫bcf(x)dx=∫acf(x)dx\int^{b}_{a}f(x…
By Joshua Siktar, Expii Team, Alex Federspiel
Problems 4
- Let fff be a continuous real function with f(2x)=3f(x)f(2x) = 3f(x)f(2x)=3f(x) for all xxx. If ∫01f(x)dx=1\int_0^1 f(x) dx = 1∫01f(x)dx=1, what is ∫12f(x)dx\int_1^2 f(x) dx∫12…
- Compute ∫03π/2∣sinx∣ dx\int_0^{3\pi/2} |\sin x| \, dx∫03π/2∣sinx∣dx.
- Compute ∫π2π∣cosx∣ dx\int_\pi^{2\pi} |\cos x| \, dx∫π2π∣cosx∣dx.
- Integrate ∫04∣x−1∣ dx\int_0^4 |\sqrt x - 1| \, dx∫04∣x−1∣dx.