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a) âˆ«(3x + 1)(2x + 1)dx

b) âˆ«3x e^(x^2) dx

c) âˆ«(4 + 3x^2) dx

d) âˆ«2cos(3x) dx

e) âˆ«(2z âˆš(4 – x^2)) dx

f) âˆ«(1/(2x^5 + 1)) dx

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01:02

Evaluate each integral.$$\int \sinh (3 x+2) d x$$

06:12

In each part, evaluate the integral, given that $f(x)=\left\{\begin{array}{ll}{2 x,} & {x \leq 1} \\ {2,} & {x>1}\end{array}\right.$$$\begin{array}{ll}{\text { (a) } \int_{0}^{1} f(x) d x} & {\text { (b) } \int_{-1}^{1} f(x) d x} \\ {\text { (c) } \int_{1}^{10} f(x) d x} & {\text { (d) } \int_{1 / 2}^{5} f(x) d x}\end{array}$$

03:01

In each part, evaluate the integral, given that $f(x)=\left\{\begin{array}{ll}2 x, & x \leq 1 \\ 2, & x>1\end{array}\right.$(a) $\int_{0}^{1} f(x) d x$(b) $\int_{-1}^{1} f(x) d x$(c) $\int_{1}^{10} f(x) d x$(d) $\int_{1 / 2}^{5} f(x) d x$

02:56

Evaluate each definite integral.$$\int_{-2}^{3}\left(-x^{2}-3 x+5\right) d x$$

Transcript

Hello. The question is taken from physics so it calculus and the question is Evaluate each integral. In discussion. We have to evaluate the value of each of these integral. So first is integration three X -1 -1 into two. x plus one N D X. This is first part. They let us solve it. Let us first multiply it. We get 66 square plus three X minus two X is plus x minus went into dx. Just normal multiplication. Now we know that in integration X to the power N dx can be written as X to the power and plus one over And the 1st 1. Okay we are using the same method here. So that is integration six outside. It’s true. The power to plus 1/2 plus one. Sorry? Okay and plus X to the power one plus 1/1 plus one minus X. To the power zero plus 1/0 plus one. So this will give you, the final solution is two x cubed plus x square by two minus X. And they let us hold the second part. Second part, the integration is three X wow E. To the power minus of two X square D X. Okay so let two x square is equal to T. So X dx is equal to D. T by four. Using this hair. So we get let us solve it. So that is integration 3/4 X. E. To the power minus T. DT. So that will be equal to minus three by four E. To the power minus of T plus C substituting T. T. Is equal to two. X squared minus 3/4. To the power minus two. X square plus C. Okay. And in a similar way. 3rd question is integration one x 2-1 And full by three x glass to buy X…

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