Question

[CALCULUS] Determine the area of the region bounded by the curves f and g for -1.5 ≤ x ≤ 0.5

Answer 1

\[f=cos(x^2)\]\[g=e^x\]

-1.5 ≤ x ≤ 0.5

Answer 2

I just need somebody to crunch the number for me. I have my answer and want to be sure I explained it right to somebody else.

Answer 3

Intercepts -1.11 and 0

Answer 4

\[\int\limits_{-1.5}^{0}\cos(x^2)-e^xdx+\int\limits_{0}^{.5}e^x-\cos(x^2)dx\]

Answer 5

Thats how I would do it, you might be able to do it with one integral instead of two but I wasnt 100% sure.

Answer 6

You need to do numerical Integration to compute the integral involving \( \cos^2(x)\)

Answer 7

You have to compute three integrals
\[\int_{-1.5}^{-1.11}
\left(e^x-\cos \left(x^2\right)\right) \, dx+
\int_{-1.1}^0 \left(\cos \left(x^2\right)-e^x\right) \, dx+

\int_0^{0.5} \left(e^x-\cos
\left(x^2\right)\right) \, dx
\]

Answer 8

All the three needs to be done with Numerical Integrtion

Answer 9

\[
\int_{-1.5}^{-1.11} \left(e^x-\cos \left(x^2\right)\right) \, dx=0.160175
\]

Answer 10

\[
\int_{-1.1}^0 \left(\cos \left(x^2\right)-e^x\right) \, dx=0.282375
\]

Answer 11

Do the third integral yourself

Answer 12

Like I said, I already did this. I was wondering what yall got for the final.

0.59

Answer 13

I helped somebody with this problem earlier. I want to verify the answer we got A = 0.59 is correct, if not I will send them the updates.

Answer 14

0.594387

Answer 15

Remember that you're approx. an area. Thus, giving an answer to 6 decimal place accuracy is stretching things quite a bit.

What do you think would be sufficient accuracy for an area approximation?