Let f be the function defined by ƒ (x) = cos( (/T). (a) Approximate the definite integral| f(x) dx using a 1 midpoint Riemann sum with the subintervals [1, 1.6], [1.6, 2], and [2, 3]. Show the work that leads to your answer. 3 (b) Approximate the definite integral | f(x) da using a 1 trapezoidal sum with the subintervals [1, 1.6], [1.6, 2], and 2, 3. Show the work that leads to your answer.

Q: 1. In the following exercises, evaluate each definite integral using the Fundamental Theorem of…

A: The general rule of integration is  ∫xndx=xn+1n+1+C Note:  According to the guidelines of the…

Q: X 0 0.5 1 1.5 F(x)

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Q: (4)Evaluate the definite integral (a)(1+ si 0 1+ sin x)dx (b) (2t+cost) di (b) f( -x/2 x+ X - dx R/4…

A: Explanation of the answer is as follows

Q: Let f be the function defined above. (a) Find the average rate of change of f on the interval -3 ≤ x…

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Q: Determine whether f(x) is differentiable at x = 0. Show your work. sin(x) cos(x)-1 3x + 1 f(x): = if…

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Q: Let f be continuous on the interval [0, b], where f(x) + f(b − x) ≠ 0 on [0, b].

A: Let I=∫0bfxfx+fb-xdx   I=∫0bfxfx+fb-xdx                     ....... (1) use ∫0afxdx=∫0afa-xdx…

Q: 3. (a) The velocity of a moving object after t seconds is given per second. Calculate the…

A: We have to find the following given condition

Q: The error in the forward approximation of the x² sin (2x) at x = π/3 is: (use function f(x) step…

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Q: (5) Find the integrals: •ftan²(x) dx ● fsec²(x) dx • ftan³(x) dx ●

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Q: Let f be the function defined above. (a) Find the average rate of change of f on the interval -3 < x…

A: To find out the average rate of change of f on the given interval.