Let F(x)= the integral from 0 to 2x of tan(t^2) dt. Use your calculator to find F″(1)

By applying the fundamental theorem of calculus, I got the derivative of the integral (F'(x)) to be 2tan(2x^2)

When I take the derivative to find F''(x) I get 8x sec^2(2x^2). When I plug 1 in for x, I don't get any of the answer choices, but I don't know where I went wrong in my evaluations. I just need to know my mistake

  1. 👍
  2. 👎
  3. 👁
  1. actually, F' = 2tan((2x)^2) = 2tan(4x^2)
    F' = 2sec^2(4x^2)(8x) = 16x sec^2(4x^2)

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    If f(x) and g(x) are continuous on [a, b], which one of the following statements is true? ~the integral from a to b of the difference of f of x and g of x, dx equals the integral from a to b of f of x, dx minus the integral from a

  2. math. PLEASE HELP.

    Question: If A= 29 degrees and a= 4.6, find c. There is a diagram shown in the textbook. b is adjacent, c is the hypotenuse, and a is opposite. I know I'm suppose to use SOH CAH TOA, and i tried using tan, but Im not getting the

  3. Calculus

    integral 1 to 500 (13^x - 11^x) + integral 2 to 500 (11^x - 13^x) dx = (answer: 14.946) I tried typing the integrals in the graphing calculator to get the answer, but it says overflow. Any help on solving this? Thanks!

  4. Trigonometry

    A calculator is broken so that the only keys that still work are the sin, cos, tan, cot, sin^-1, cos^-1, and tan^-1 buttons. The display initially shows 0. In this problem, we will prove that given any positive rational number q,

  1. trigonometry

    How do you find: cot(-5pie/4)? you have to know that cotx = 1/tanx so you could just trustfully change your calculator to radians enter 5*pi/4, press =, press +/-, then press Tan, =, then the 1/x key you should get -1 or... you

  2. Calculus

    Calculate the following integral: ∫ sec^4 (3x)/ tan^3 (3x) dx For this one, can I bring up the tan to tan^-3?

  3. Calculus

    I am trying to find the integral of e^(6x)sin(7x). Apparently, the answer is (6e^(6x)sin(7x) - 7e^(6x)cos(7x))/85) + C and achieving the answer is mostly understandable since it involves integrating the function in parts... that

  4. calc

    Let F of x equals the integral from 1 to 3 times x of the natural logarithm of t squared. Use your calculator to find F″(1).

  1. trig

    find the exact value of each expression. do not use a calculator. Sec 3.14/4 + 2 csc 3.14/3 4 + tan 2*3.14/3

  2. Calculus

    Find the length of the curve correct to four decimal places. (Use a calculator to approximate the integral.) R(t)=(t^2,t^3,t^4) 0

  3. Calculus

    Using the Fundamental theorem of Calculus find the derivative of F(x) = sec(3x) + ∫ [e^-(t^(2))] Integral from ( 0 to tan(3x) ) f(x) = sec(x) f'(x)= sec(x)tan(x) and according to the fundamental ToC, u plug the x value of the

  4. integral confusion

    integral of Sec[2x]Tan[2x] i know u is sec 2x du=2sec2xtan2x dx what would i have to multiply with du so it would equal tan 2x dx? if my question is confusing, then here's another example of what i'm talking about: integral of

You can view more similar questions or ask a new question.