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use the limit definition of definite integral to evalute int_{0}^{1} (2x+3)dx
help me please
 one year ago
 one year ago
use the limit definition of definite integral to evalute int_{0}^{1} (2x+3)dx help me please
 one year ago
 one year ago

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saifoo.khanBest ResponseYou've already chosen the best response.0
\[\int\limits_{0}^{1} (2x+3)dx\]Like this, right?
 one year ago

saifoo.khanBest ResponseYou've already chosen the best response.0
Now we have to integrate that then install the limits 1 and 0. Agree?
 one year ago

saifoo.khanBest ResponseYou've already chosen the best response.0
Okay, so integral will be: \[[\frac{2x^2}{2}+ 3x]^1 _0\]
 one year ago

hamsaBest ResponseYou've already chosen the best response.0
no please not in this way for rumin sum
 one year ago

hamsaBest ResponseYou've already chosen the best response.0
thank you for picture alredy i solve it like you and get 4 but in this case want to solve in rieman sum
 one year ago

hamsaBest ResponseYou've already chosen the best response.0
please help me i wail waiting
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
\[f(x)=2x+3,a=0,b=1,\Delta x = \frac{1}{n}\]
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
\[x_i=a+i \Delta x\]compute \[f(x_i)\]and plug everything into \[\lim_{n \rightarrow +\infty}\sum_{i=1}^{n}f(x_i) \Delta x\]
 one year ago

hamsaBest ResponseYou've already chosen the best response.0
i don't know what you mean for xi
 one year ago

hamsaBest ResponseYou've already chosen the best response.0
so could you tell me how i will start the formula and with pluging number please
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
\[x_i=a+i \Delta x = 0 + i (\frac{1}{n})=i(\frac{1}{n})\] \[f(x)=2x+3\]\[f(x_i)=2(x_i)+3 = 2\left(i (\frac{1}{n})+3\right)=\frac{2}{n}i+3\]
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
sorry, the closing parenthesis ) should be before +3, not after +3.
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
\[f(x_i) \Delta x=\left(\frac{2}{n}i + 3\right)(\frac{1}{n})\]
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
just expand, apply the \(\lim_{n \rightarrow \infty} \sum_{i=1}^n\) on the expression, and evaluate the limit.
 one year ago
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