Answer:
Explanation:
The definite integral of the function (2x - 3) with respect to x can be found using the antiderivative, also known as indefinite integration.
The antiderivative of (2x - 3) is:
x^2 - 3x + C, where C is the constant of integration.
For the definite integral, we need to find the antiderivative over a given interval. To calculate the definite integral, we need to evaluate the antiderivative at the limits of the interval and subtract the values.
So, for example, if the interval is from a to b, the definite integral is given by:
∫_a^b (2x - 3) dx = (x^2 - 3x) |_a^b = (x^2 - 3x) evaluated at b - (x^2 - 3x) evaluated at a.
The definite integral of the function y³ (2y² – 3) with respect to y can be found in a similar way. The antiderivative of y³ (2y² – 3) can be found using power rule of integration.
The antiderivative of y³ (2y² – 3) is:
(1/4) y⁴ - 3y² + C, where C is the constant of integration.
The definite integral of the function can then be found by evaluating the antiderivative at the limits of the interval and subtracting the values, as described above.