Question

I need help with a calculus question. I know all the steps to get the answer (which i will post) I just dont understand them. So it should be a pretty easy problem to help with

Answer 1

evaluate the definite integral by the limit definition.
the problem is \[\int\limits_{4}^{10} 6 dx\]

Answer 2

step 1: y=6 on [4,10]

(note: \[\Delta x=\frac{ 10-4 }{ n }=\frac{ 6 }{ n } , \left| \left| \Delta \right| \right| \rightarrow 0 (as) n \rightarrow \infty \]

Answer 3

which part do you need explanation?

Answer 4

all of it. im not sure of why anything is done. do you want me to finish putting the steps up?

Answer 5

in order to evaluate the integral, absent formulas to evaluate it, you have to resort to using the limit definition of the integral.

Answer 6

to solve\[\int_4^{10} 6 dx\] is to evaluate \[\lim_{ n \rightarrow +\infty} \sum_{i=1}^{n}6 \Delta x\]

Answer 7

\[\sum_{i-1}^{n} F(c _{i}) \Delta x _{i}\]

\[\sum_{i-1}^{n} f(4+\frac{ 6i }{ n })(\frac{ 6 }{ n } ) \]

\[\sum_{i-1}^{n} 6 (\frac{ 6 }{ n })\]

\[\sum_{i-1}^{n}\frac{ 36 }{ n }\]

\[\frac{ 1 }{ n }\sum_{i-1}^{n}36\]

\[\frac{ 1 }{ n }(36n)\]

=36

Answer 8

the rest of the steps :)

Answer 9

we state for the record (^^) \(f(x)=6,\,a=4,\,b=10\) then compute the parts of the limit definition.

Answer 10

\[\Delta x=\frac{6}{n}\]