Diffentiating the differential element!

Calculus Level 2

Evaluate of the below given expression.

d d x ∫ 0 π 6 sin ⁡ 2 x + cos ⁡ 2 x t a n x − 1 d x \dfrac{d}{dx}\int_0^{\dfrac{\pi}{6}}\dfrac{\sin^2x+\cos2x}{tanx-1}dx

π \pi − 1 -1 0 0 2 2 2 π 2\pi

Skanda Prasad by Skanda Prasad , 20, 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.

2 solutions

Skanda Prasad
Oct 8, 2017

Don't bother evaluating the integral...

The value of the integral is a constant say k \color{#D61F06}k because limits are applied to the integral.

Hence,

d d x ( k ) \dfrac{d}{dx}\color{#D61F06}(k) = 0 =\boxed{0}

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Max Ranis
Oct 8, 2017

It may be a point of interest however that the integral is undefined at π 4 \frac{\pi}{4} so we should not be able to take a derivative of an undefined quantity.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...