let-f-a-0-pi-2-dx-a-sinx-a-real-1-find-a-explicit-form-for-f-a-2-calculste-also-g-a-0-pi-2-dx-a-sinx-2-and-h-a-0-pi-2-dx-a-sinx-3-3-give-f-n-a-at

Question Number 68869 by mathmax by abdo last updated on 16/Sep/19

l e t f (a) = \int_{0}^{\frac{π}{2}} \frac{d x}{a + s i n x} (a r e a l)

1) f i n d a e x p l i c i t f o r m f o r f (a)

2) c a l c u l s t e a l s o g (a) = \int_{0}^{\frac{π}{2}} \frac{d x}{{(a + s i n x)}^{2}} a n d h (a) = \int_{0}^{\frac{π}{2}} \frac{d x}{{(a + s i n x)}^{3}}

3) g i v e f^{(n)} (a) a t f o r m o f i n t e g r a l

4) f i n d t h e v a l u e s o f i n t e g r a l s \int_{0}^{\frac{π}{2}} \frac{d x}{3 + s i n x}, \int_{0}^{\frac{π}{2}} \frac{d x}{{(3 + s i n x)}^{2}}

a n d \int_{0}^{\frac{π}{2}} \frac{d x}{{(3 + s i n x)}^{3}}