How about drawing sum upper and lower sums! You won't get very far because you'll be married to the horizontal axis and then, of course, all of the sums are zero and since a definite integral is always sandwiched between any upper and any lower sum. The value is trapped by 0. I.E. 0 <= the integral <= 0.

2014年2月5日 · $\begingroup$ Integral from 0 to... 0. $\endgroup$ – Martín-Blas Pérez Pinilla. Commented Feb 4, 2014 ...

2017年11月14日 · Prove that an integral $$\int_0^{\pi/2} \cos^{10}x\cdot \cos(12x)\,\text{d}x=0$$ I'm sorry but I am completely lost.

2015年4月12日 · For an odd function, I know that f(x) = - f(x). I'm trying to show that $\int^{a}_{-a} f(x) dx$ = 0. I've seen the proof where it splits the integral up into: $$\int^{a}_{0} f(x) dx + \int^{0}_...

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It doesn't mean anything special. Maybe one could have detected that the value of the integral is $0$ using symmetry considerations, making the actual computation of the integral superfluous. Things start to get interesting if the integral is $0$ for all closed curves, not just a particular one. A necessary condition for this would be that your ...

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2015年9月12日 · Integral from 0 to 1 1/x. Ask Question Asked 9 years, 5 months ago. Modified 9 years, 5 months ago. Viewed ...

2018年7月22日 · The integral you wonder about is: $$\int_0^1e^{y^2} \sin(y)\textrm dy, $$ And the function here is always positive in the domain $[0,1]$. Hence, the integral will not be zero. Be aware, however, that it is unclear which limits belong to which variable. It might be better to write $$\int_{-1}^1\textrm dx\int_0^1\textrm dy\, e^{x^2+y^2} \sin(y), $$