Definite and indefinite integrals
Definite and indefinite integrals are fundamental concepts in calculus, each serving distinct purposes in mathematical analysis. Indefinite integrals, also known as antiderivatives, represent families of functions whose derivatives yield a given function. On the other hand, definite integrals compute the accumulated area under a curve over a specific interval, providing precise numerical values. Together, these concepts form the backbone of integral calculus, facilitating the analysis of functions, computation of areas, and solving a wide array of mathematical problems. Understanding their distinctions and applications is essential for mastering the intricacies of calculus.
Questions
- What is the antiderivative of #g(x) = x ^ π#?
- How do you evaluate the integral of #int tan(x)ln(cosx) dx#?
- If the integral [0,3] of f(x)dx=4, the integral [3,6] of f(x)dx=4, and the integral [2,6] of f(x)dx=5, then what does the integral [0,2] of f(x)dx=?
- How do you evaluate the definite integral #int (-2x^2+3x+2)dx# from [0,2]?
- What is the integral of #int f(x)=e^(3x)# from 0 to 2?
- What is the integral of #int sec(x)# from 0 to 2?
- How do you evaluate the definite integral #int (x-2) dx# from [-1,0]?
- How do you evaluate the indefinite in integral? Use C for constant integration
- How do you evaluate #int (x^2-1)/( x+1) dx# for [1, 2]?
- How do you evaluate the integral #(1+tan(x))^3 * sec^2(x)dx# within the range [0,pi/4]?
- How do you find the integral of #int cscx dx# from pi/2 to pi?
- How do you evaluate the definite integral #int 2^x dx# from #[-1,1]#?
- What is the integral of #int cos^3 (x)dx# from 0 to pi/2?
- If # int_0^3 f(x) dx = 8 # then calculate? (A) (i) #int_0^3 2f(x) dx#, (ii) #int_0^3 f(x) + 2 dx# (B) #c# and #d# so that #int_c^d f(x-2) dx #
- Help me please? with indefinite integral ln(cosx)dx/cos^2x
- How do you evaluate the definite integral #int x^2 dx# from #[0,1]#?
- How do you find the indefinite integral of #int (x+1/x)^2dx#?
- How do you evaluate the integral of #int x/[(x^2)+1]dx#?
- Evaluate the integral of (x√x-3dx)?
- Find the indefinite integral. (Note: Solve by the simplest method—not all require integration by parts. Use C for the constant of integration.)?