I need help for 2 homework problems. No matter what I do, I can't get the correct answer. I know that you have to use inverse trig functions, but I'm still not getting the correct answer.
1) f'(t)=20/(1+t^2) such that f(1)=0
2) 4/(squareroot(1-x^2)) such that f(1/2) = 1
Uh, I've asked questions here before, but people tend to only give me the answer to my questions. Could you explain the steps you took to get to the answer? I've taken calculus in high school, but totally forgot everything.
1) f'(t)=20/(1+t^2) such that f(1)=0
2) 4/(squareroot(1-x^2)) such that f(1/2) = 1
Uh, I've asked questions here before, but people tend to only give me the answer to my questions. Could you explain the steps you took to get to the answer? I've taken calculus in high school, but totally forgot everything.
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1)
f '(t)=20/(1+t^2)
Integrate,
∫ 20/(1+t^2)
Now I take out the 20, so it's easier to integrate in respect to the inverse trig rule for tan. SO,
20 ∫ 1/(1+t^2)
Integrating 1/(1+t^2) with respect to t gives tan^-1 t + C where tan^-1 is inverse tan and C is some constant. BUT you must times by 20 as you took it out, so f(t) = 20tan^-1 t + C
When f(1) = 0,
Enter in calculator
0 = 20tan^1 (1) + C
0 = 20*(π/4) + C
0 = 5π + C
C = -5π (where π = pi)
Therefore the function is 20tan^-1 t + 5π
2)
f '(x) = 4/(squareroot(1-x^2))
Integrate, similar to above.
∫4/(squareroot(1-x^2))
Take out the 4, so 4∫1/(squareroot(1-x^2))
integrate with respect to x gives sin^-1x (where sin^-1 is inverse sin).
Times through by 4
f(x) is 4sin^-1 x + C
When f(1/2) = 1
1 = 4*sin^-1 (1/2) + C
enter in calculator.
1 = 4* π/6 + C
1=2π/3 + C
C = -1.094....
Therefore f(x) = 4*sin^-1 x - 1.094
What are your answers? Make sure if you are calculating in a scientific calculator, your calculator is in RADIANS.
f '(t)=20/(1+t^2)
Integrate,
∫ 20/(1+t^2)
Now I take out the 20, so it's easier to integrate in respect to the inverse trig rule for tan. SO,
20 ∫ 1/(1+t^2)
Integrating 1/(1+t^2) with respect to t gives tan^-1 t + C where tan^-1 is inverse tan and C is some constant. BUT you must times by 20 as you took it out, so f(t) = 20tan^-1 t + C
When f(1) = 0,
Enter in calculator
0 = 20tan^1 (1) + C
0 = 20*(π/4) + C
0 = 5π + C
C = -5π (where π = pi)
Therefore the function is 20tan^-1 t + 5π
2)
f '(x) = 4/(squareroot(1-x^2))
Integrate, similar to above.
∫4/(squareroot(1-x^2))
Take out the 4, so 4∫1/(squareroot(1-x^2))
integrate with respect to x gives sin^-1x (where sin^-1 is inverse sin).
Times through by 4
f(x) is 4sin^-1 x + C
When f(1/2) = 1
1 = 4*sin^-1 (1/2) + C
enter in calculator.
1 = 4* π/6 + C
1=2π/3 + C
C = -1.094....
Therefore f(x) = 4*sin^-1 x - 1.094
What are your answers? Make sure if you are calculating in a scientific calculator, your calculator is in RADIANS.
-
Integrate and solve for C.
For example, on your first question it tells you that f(1) = 0. After you integrate f'(t), plug in 1 for t and set the equation equal to 0. Then, solve for C. After you get a value for c, you can replace c with that value in your integrated equation of f'(t).
I believe that's how you solve them. Anyone, feel free to correct me if I'm wrong.
For example, on your first question it tells you that f(1) = 0. After you integrate f'(t), plug in 1 for t and set the equation equal to 0. Then, solve for C. After you get a value for c, you can replace c with that value in your integrated equation of f'(t).
I believe that's how you solve them. Anyone, feel free to correct me if I'm wrong.