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Evaluate the integral_ L f(x) dx where f(x) = (3 if -3 < x < 0 4 - x2 if 0 < x < 4...

Question

Evaluate the integral_ L f(x) dx where f(x) = (3 if -3 < x < 0 4 - x2 if 0 < x < 4

Evaluate the integral_ L f(x) dx where f(x) = (3 if -3 < x < 0 4 - x2 if 0 < x < 4



Answers

Evaluate the definite integral of the given piecewise-continuous function $f$. $$ \int_{0}^{3} f(x) d x, \text { where } f(x)=\left\{\begin{array}{ll} 4, & 0 \leq x<2 \\ 1, & 2 \leq x \leq 3 \end{array}\right. $$

In the given question you have to find the value of integration from 3 to 0. Okay. And uh function is fx or dx And it is given to you that it is given to you that same integration of the function in the limits of 0 to 3 years? It was 24 No. To provide the answer, I am using a property property number Second states that if you are integrating in the limits of it will be of a function. And if you interchange the limits that are from B to A then you can say that sign of the integration changes. Okay. So by this property I can say that integration of the function in the limits of 3 to 0 should be. It was two minus of integration in the limits of 0 to 3 fx or dx. And this integration here is provided you that if it was 24 So finally we can say that the answer of this question should be here minus four. Okay. I had calculated it by the help of property number. Second, Thank you.

In this question that is asked to find the definite integration of 0-4 in the function minus three X plus four. More or less. First of all I'm going to write the short but that says that anti develop you of models of X plus B is given by one x 2 a. It's let's be into more or less of X. Let's be So you can see it on there. If we substitute the values we get one by going to -3 and -3 x plus four into models or minus three X plus four. And in this end of the video we have to apply the fundamental terms of calculus. That says that first of all we have to substitute of Parliament so we can see we get after substituting for here minus well plus four in two. Models of minus world class sport. Then we have to substitute zero. So we get four in two models of four. And now this turns out into -1 x six and -18 to Let's say 30 to -64 and minus 16 and That is equals 2 -1 by 60 And -80. This turns out to 40 Vitaly So 40 way three is the final answer for this question here thank you

Again this question. We have to solve integration. 0 to 4 X cubed DX. OK, so in discussion. First, we will solve the integration of X cubed DX. And then we will apply the limits and the limits are 0 to 4. Okay, so integration 024 X cube X cubed DX. It will be okay. First time writing down the formula hair. The integration of access to the power index will be expressed the rest of the power and plus one divided by one plus one plus c. And it will be expressed to the power three plus one divided by three plus one. And we will not apply this constant here because we have the limits. So this is 0 to 4. Okay? And now it will be access to the power four divided by four and the limited 0 to 4. Okay, so it will be won by four. First of all, a parliament that is four raised to the power four minus one by four. And the lower limit that is zero raised to the power for okay. And now it will be won by 44 raised to the power four. So it will be 4.4 dot 4.4. Okay? Divided by four minus zero and one for the skill we cancel and 4.4 dot four. It will be 64 we can say the integration of X cubed DX with limits 0 to 4. It will be 64. And this will be your final answer. Thank you.

Hello Friends. We have to value the given definite. And Eagle. That is 0 to 1 four X. Into three X squared minus. Fun. To the power of three d. x. Okay so we will substitute three X. Discriminates one by you. So this will be six XL for dx equals two. Do you? So acts of D. x equals two. one x 6 of D. U. So we can write it one x 4 x six of here too. The poverty do you Who went X. zero then limited. You will be monitored for. Okay when exit comes to one then the limit of you will be two. Mhm. So this will be You to devote four upon 4. My husband too. So this will be considered to buy three into one x 4. Now we will put the limit that is to the power of the world manus off management. To the power of food. So this will be cause to one up 1 six to the power of 16- of one That is 15 upon six. So this is the answer I hope you initialed. Thank you.


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