Question

### Gauthmathier8001

Grade 9 · 2021-02-01

If g'\left (x \right )=\cos (\pi x^{2}+1) and g(1)=\dfrac {1}{2}, then g\left (2 \right ) = （ ）

Good Question (103)

Answer

4.9(224) votes

### Gauthmathier9317

Grade 9 · 2021-02-01

Answer

D

Explanation

Note that \int _{1}^{2}g'\left (x \right )\d x=g(2)-g(1).

Therefore, \int _{\ 1}^{2}\cos (\pi x^{2+1})\d x=g(2)-\dfrac {1}{2}, or g(2)=\int _{1}^{2}\cos (\pi x^{2+1})\d x+\dfrac {1}{2}. Using your graphing calculator, you have \int _{\ 1}^{2}\cos (\pi x^{2+1})\d x\approx 0.18126. Thus, g(2)\approx 0.18126+\dfrac {1}{2}\approx 0.681.

Therefore, \int _{\ 1}^{2}\cos (\pi x^{2+1})\d x=g(2)-\dfrac {1}{2}, or g(2)=\int _{1}^{2}\cos (\pi x^{2+1})\d x+\dfrac {1}{2}. Using your graphing calculator, you have \int _{\ 1}^{2}\cos (\pi x^{2+1})\d x\approx 0.18126. Thus, g(2)\approx 0.18126+\dfrac {1}{2}\approx 0.681.

Thanks (77)

Does the answer help you? Rate for it!

## Still Have Questions?

Find more answers or ask new questions now.