Please solve.

Use the formal definition of the definite integral (page 378) to find the exact value of the definite integral _ (x2 + 3x)dx.TOC Go to pg. 378 1 AA B 5.2 The Definite Integral We saw in Section 5.1 that a limit of the form 1 lim f(x; ) As = lim [f(x;) Ax + f(x;) Ax + ...+ f(a;) Ax] 71 100 i= 1 13-+00 arises when we compute an area. We also saw that it arises when we try to find the distance traveled by an object. It turns out that this same type of limit occurs in a wide variety of situations even when f is not necessarily a positive function. In Chapters 6 and 8 we will see that limits of the form (1) also arise in finding lengths of curves, volumes of solids, centers of mass, force due to water pressure, and work, as well as other quantities. We therefore give this type of limit a special name and notation.E TOC Go to pg. 378 Or AA B [2 Definition of a Definite Integral If f is a function defined for a 0 there is an integer / such thatTOC Go to pg. 378 U AA B f(z) da - 1=1 for every integer n > N and for every choice of a* in [;-1, x]. Note 1 The symbol / was introduced by Leibniz and is called an integral sign. It is an elongated S and was chosen because an integral is a limit of sums. In the notation / f(x) dx, f(x) is called the integrand and a and b are called the limits of integration; a is the lower limit and b is the upper limit. For now, the symbol da has no meaning by itself; / f(x) dx is all one symbol. The de simply indicates that the independent variable is c. The procedure of calculating an integral is called integration. 0, the Riemann sum _ f(a* ) Ax is the sum of areas of rectangles. 0, the integral f (z) da is the area under the curve a y = f(x) from a to b. y =f(x) b X