EXAMPLE 4 Use the Table of Integrals to find SxVx² + 4x + 11dx. Since the table gives forms involving a² + x², V a² - x², and Vx - a?, but not v ax² + bx + c, we first complete the square. x? + 4x + 11 = (x + 2)² + 7 If we make the substitution u = x + 2 (so x = u - 2), the integrand will involve the pattern va + u². SxVx + 4x + 11dx = S( Vu– 2 x )Vư² + 7du = S u² + 7du – 2 | × Vư² + 7du - 2 SVūt + 7du The first integral is evaluated using the substitutiont = u² + 7. 1 Suvu + 7du =SVtdt 2 t (u² + 7) 3 For the second integral we use Formula 21 with a = v7. 7. Vu? + 7du = 5Vu² + 7+;In (u + Vu² +7) II

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A: Please refer the attached image for complete solution.

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A: To solve the given integral.

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Q: 3. (Section 4.1) Evaluate each indefinite integral. (a) /202 (b) /(3e* + 2)dr 4x (c) / (182² + 6x +…

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.