Question

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Answer 1

The derivative of the function g(x) as given in the task content by virtue of the Fundamental theorem of calculus is 6.1820.

What is the derivative of the function g(x) by virtue of the Fundamental theorem of calculus as given in the task content?

g(x) = Integral; √2 ln(t) dt (with the upper and lower limits e^x and 1 respectively).

Since it follows from the Fundamental theorem of calculus that given an integral where;

Now, the midpoint rule approximation,

$\int\limits^a_b {x} \, dx = \sum f ( x_i + x_{i + 1})/ 2$

$\int\limits^8_0 {sin \sqrt{x} } \, dx = \sum f ( x_i + x_{i + 1})/ 2\\\\\\\int\limits^8_0 {sin \sqrt{x} } \, dx = (0.8415 + 0.9870 + 0.786 + 0.475)(2)\\\\\int\limits^8_0 {sin \sqrt{x} } \, dx = 6.1820$

The derivative of the function g(x) as given in the task content by virtue of the Fundamental theorem of calculus is 6.1820.

Read more on fundamental theorem of calculus;

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