Calculator Active. Using a Left Hand Riemann Sum with 6 sub-intervals of equal width, approximate the area bound by the function f(x) = 9 – x², the x-axis, and the lines x=0 and x=3. Round your answer to 3 decimal places.
Riemann Sum
Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus.
Riemann Integral
Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.
Given ,
Hence,
Now, break the interval into subinterval, which is given below.
Hence, the area by using left hand Riemann sum is given by
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