Use FTC to evaluate a definite integral with basic integrand--
(integral) bottom number 0, top #2 (4x^3+1)dx=
Don't know what FTC stands for but
the integral of 4x^3 + 1 is
x^4 + x
so the definite integral of the above from 0 to 2 is
(2)^4 + 2 - 0
= 18
FTC is the Fundamental Theorem of Calculus. Thanks for you help.
To evaluate the definite integral using the Fundamental Theorem of Calculus (FTC), you need to follow these steps:
Step 1: Find the antiderivative of the integrand.
The antiderivative of 4x^3+1 is (4/4)x^4 + x = x^4 + x.
Step 2: Evaluate the antiderivative at the upper limit (2) and subtract the value of the antiderivative at the lower limit (0).
Substituting 2 into the antiderivative function, we get: (2^4 + 2) = 16 + 2 = 18.
Substituting 0 into the antiderivative function, we get: (0^4 + 0) = 0 + 0 = 0.
Step 3: Subtract the lower limit evaluation from the upper limit evaluation.
18 - 0 = 18.
Therefore, the value of the definite integral ∫(0 to 2) (4x^3+1)dx is equal to 18.