Calculus true or false

Calculus Level 1

True or false :

Using the first fundamental theorem of calculus ,
If f ( x ) d x = F ( x ) + c \displaystyle \int f(x)dx = F(x) + c

a b f ( x ) d x = F ( b ) F ( a ) \displaystyle \int_{a}^{b} f(x) dx = F(b) - F(a)

We can evaluate the following integral as follows

1 1 1 x 2 d x = 2 \displaystyle \int_{-1}^{1} \dfrac{1}{x^{2}} dx = -2

False True

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1 solution

Franz Pabilona
May 1, 2016

False. The interval of integration [-1 , 1] contains 0 at which function 1 / x2 is discontinuous and the above theorem cannot be applied.

But looking it in a limit way, it does equal to -2... :)

muren kang - 1 year, 11 months ago

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