Final answer:
To calculate the integral using left-hand approximation, you can use the trapezoidal rule, Simpson's rule, sum of left-hand rectangles, or finding the antiderivative and evaluating.
Step-by-step explanation:
To calculate the integral using left-hand approximation, there are several methods you can use:
A) Trapezoidal Rule: This method approximates the area under the curve by dividing it into trapezoids. You calculate the area of each trapezoid and sum them up to get the total approximation. This method is fairly accurate but still an approximation.
B) Simpson's Rule: This method uses parabolic curves to approximate the area under the curve. It provides a more accurate result than the trapezoidal rule. The curve is divided into multiple segments, and the area of each segment is calculated using Simpson's rule. The sum of these areas gives the final approximation.
C) Sum of Left-hand Rectangles: This method approximates the area under the curve by dividing it into a series of rectangles. Each rectangle's height is the left-hand endpoint of the corresponding interval, and the width is the interval size. The areas of these rectangles are then summed up.
D) Finding the Antiderivative and Evaluating: This method involves finding the antiderivative of the function and evaluating it between the given limits. This method provides an exact result, but it requires integration techniques.