Integration(think differently)

Calculus Level 5

If I = ∫ ( 5 − x ) ( 2 + x ) . d x \int \sqrt \frac{(5-x)}{(2+x)} .dx is of the form I = ( x + a ) ( b − x ) + c sin ⁡ − 1 x + d e + k I=\sqrt (x+a) \sqrt (b-x)+c\sin^{-1} \sqrt \frac{x+d}{e} +k where k is constant of integration. Find a + b + c + d + e a+b+c+d+e


The answer is 23.

Tanishq Varshney by Tanishq Varshney , 23, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Tanishq Varshney
Jan 26, 2015

Put x + 2 = t 2 x+2= t^2

d x = 2 t d t dx=2t dt

The integration is reduced to

2 ∫ 7 − t 2 d t 2\int \sqrt{7-t^2} dt

Apply the formula. Plz upvote if u liked my solution

4 Helpful 0 Interesting 0 Brilliant 0 Confused

We can also make a substitution x = 5 cos ⁡ 2 θ − 2 sin ⁡ 2 θ x = 5\cos^2{\theta} - 2\sin^2{\theta}

Rajdeep Dhingra - 6 years, 3 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...