Find the Exact Area Under the Curve Using Integration Questions

Description

  find the area and answer questions.

Find the approximate area under the curve by dividing the intervals into LaTeX: nn subintervals and then adding up the areas of the inscribed rectangles. The height of each rectangle may be found by evaluating the function for each value of x. Your instructor will assign you LaTeX: n_1n 1and LaTeX: n_2n 2.

n1=6 n2=12

LaTeX: y=2x\sqrt{x^2+1}y = 2 x x 2 + 1  between LaTeX: x=0x = 0 and LaTeX: x=6x = 6 for LaTeX: n_1n 1and LaTeX: n_2\:n 2

Find the exact area under the curve using integration LaTeX: y=2x\sqrt{x^2+1}y = 2 x x 2 + 1 between LaTeX: x=0x = 0 and LaTeX: x=6x = 6

Explain the reason for the difference in your answers.