Question

can someone help me with some integrals

Answer 1

okay dear bring it on

Answer 2

http://prnt.sc/b3h2ub 37

Answer 3

Sorry, it's all blurry.
Is it \[\int\limits_{0}^{1}(x^{e}+e ^{x})dx\]

Answer 4

yes

Answer 5

Ok, we can separate this integral into two;\[\int\limits_{0}^{1}(x^e+e^x)dx=\int\limits_{0}^{1}x^edx+\int\limits_{0}^{1}e^xdx\]First one is easy:\[\int\limits_{ }^{ } x^edx=\frac{ x ^{e+1} }{ e+1 }+ С\]Second is simple too: \[\int\limits_{ }^{ } e ^{x}dx= e^{x} + C\]Now we use the intervals:\[\frac{ x ^{e+1} }{ e+1 } + C= \frac{ 1^{e+1} }{ e+1 } + C - \frac{ 0^{e+1} }{ e+1 } - C = \frac{ 1 }{ e+1 }\]And\[e ^{x}+C= e ^{1}+C-e ^{0}-C = e-1\]So the answer is \[e-1 +\frac{ 1 }{ e+1 }\]

Answer 6

that is the answer for no. 21 question

Answer 7

the solving is in the attached

Answer 8

is this the right question for no.25\[\int\limits_{\frac{ \pi }{ \theta }}^{\pi}\sin \theta d \theta \]

Answer 9

its not really clear

Answer 10

Niyex, 0 power any number is 0, so the right answer for no. 21 is 2.
No.25 is \[\int\limits_{\pi/6}^{\pi} \sin \theta d \theta \]

Answer 11

niyex \(0^x=0\). So there won't be anything left to subtract from the left hand side.

Answer 12

ohohohoho am so sorry Yagosik so so sorry a mistake you are correct

Answer 13

this is the correct working modified. Thanks yagosik... and Sachintha

Answer 14

integrate \[x^{x}\]

Answer 15

integrate x^x

Answer 16

no.27 \[\int\limits \left( u+2 \right)\left( u-3 \right)du\] here is the working in the attached file