The problem is to evaluate the integral 10secxtanx dx, from -1/7 pi to 3/8 pi.

What I've done so far is evaluated the integral since secxtanx is a trig identity, so the integral of that is secx. I took out the 10 since it was a constant which leaves me with 10[sec(3/8)pi - sec(-1/7)pi]. Since those values aren't part of the unit circle, I put that in my calculator and came up with the answer 15.03209666, however the program that has my question is not accepting this answer. My calculator is in radians.

Please post the last sentence of the question.

Did the program ask you to give the answer to 4 places after the decimal, or does it ask you to give an exact answer?

The program is on the UT website, and it takes answers within 1% of the actual answer. And that's all to the question.

As far as I can see, your analytic answer and numerical approximation are both correct. It has to have something to do with the answering instructions. Does it have the capacity to accept the exact (analytic) answer?

Yes, it can take decimal places pretty far, even a rounded answer is still within 1% of the answer I received. So, I am unsure what the problem is, I am still awaiting an email from my professor and TA as to what could be the problem.

I agree with MathMate,

I got exactly the same answer right to the last decimal place.

To evaluate the integral 10sec(x)tan(x)dx over the interval from -1/7 pi to 3/8 pi, you correctly recognized that sec(x)tan(x) is a trigonometric identity.

Now, when you evaluate the integral of sec(x)tan(x)dx, the antiderivative is sec(x), as you stated. However, we need to apply the Fundamental Theorem of Calculus to evaluate the definite integral over the given interval.

To do this, we substitute the limits of integration into the antiderivative and evaluate it at those points.

So, let's evaluate the definite integral step by step:

1. Evaluate sec(3/8 pi) - sec(-1/7 pi).

- Note that sec(3/8 pi) means finding the value of sec(x) at x = 3/8 pi, and sec(-1/7 pi) means finding the value of sec(x) at x = -1/7 pi.

2. To find the values, use your calculator in radian mode.

- Make sure that your calculator is set to radians, as you mentioned.

3. Calculate sec(3/8 pi) and sec(-1/7 pi) using your calculator.

4. Then subtract sec(-1/7 pi) from sec(3/8 pi).

- This gives you the value of the integral within the given interval.

Now, from what you mentioned, you input the values into your calculator and obtained the answer 15.03209666. However, it seems that the response from the program did not accept this answer.

To resolve this issue, I would suggest checking if you made any errors while entering the values into the calculator or if there were any rounding differences. Also, ensure that the program is expecting the answer to a certain number of decimal places.

Double-check your calculations to ensure that you have the correct numerical value for the definite integral.