Mathematics, 24.08.2020 02:01 633242
Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the value of n. Round the answers to four decimal places and compare the results with the exact value definite integral. ∫9 4 √xdx, n=8.
Answers: 2
![\int\limits^a_b {f(x)} \, dx = \frac{b-a}{2n}[f(x_{0})+2f(x_{1})+2f(x_{2})+...+2f(x_{n-1})+f(x_{n})]](/tpl/images/0728/1046/de6f2.png)
![\int\limits^9_4 {\sqrt{x} } \, dx = \frac{9-4}{2.8}[2+2.\sqrt{5} +2.\sqrt{6} +2.\sqrt{7}+2.\sqrt{8}+3]](/tpl/images/0728/1046/caa58.png)
![\int\limits^9_4 {\sqrt{x} } \, dx = \frac{5}{16}[25.3193]](/tpl/images/0728/1046/4ff29.png)
![\int\limits^a_b {f(x)} \, dx = \frac{b-a}{3n}[f(x_{0})+4f(x_{1})+2f(x_{2})+...+2f(x_{n-2})+4f(x_{n-1})+f(x_{n})]](/tpl/images/0728/1046/219db.png)
![\int\limits^9_4 {\sqrt{x} } \, dx = \frac{9-4}{3.8}[2+4.\sqrt{5} +2.\sqrt{6} +4.\sqrt{7} +4\sqrt{8} +3]](/tpl/images/0728/1046/c3c31.png)
![\int\limits^9_4 {\sqrt{x} } \, dx = \frac{5}{24}[40.7398]](/tpl/images/0728/1046/04956.png)
![\int\limits^9_4 {\sqrt{x} } \, dx = \frac{2.\sqrt[]{x^{3}} }{3}](/tpl/images/0728/1046/22ff0.png)
![\int\limits^9_4 {\sqrt{x} } \, dx = \frac{2.\sqrt[]{9^{3}} }{3}-\frac{2.\sqrt[]{4^{3}} }{3}](/tpl/images/0728/1046/a74d6.png)
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