(a) We define the improper
where Da is the disk with radius a and center the origin. Show that
(b) An equivalent definition of the improper integral in part (a) is
where Sa is the square with vertices (±a, ±a). Use this to show that
(c) Deduce that
(d) By making the change of variable
(This is a fundamental result for probability and statistics.)
Want to see the full answer?
Check out a sample textbook solutionChapter 15 Solutions
CALCULUS,EARLY TRANS LCPO
- Calculate the line integral f (2x²y + 10x + 6y − 6) dx + (−6xy + 7) dy, - where C' is the rectangle with vertices (−1, 1), (−1, 2), (-4,2), and (-4, 1) oriented clockwise. Enter an exact answer. Provide your answer below: fc(2x²y + 10x + 6y - 6) dx + (−6xy + 7) dy =arrow_forward(a) Verify that the Fundamental Theorem for Line Integrals can be used to evaluate the integral Sc ey dx + e dy, where C is the parabola r(t) =, for –1arrow_forwardb) Calculate the line integral of F along the boundary of the rectangle [0, 1 x[-1, 2], traversed once in the clockwise direction.arrow_forwardEvaluate the line integral (3ry² + 6y) dr, where C is the path traced by first moving from the point (-3, 1) to the point (2, 1) along a straight line, then moving from the point (2, 1) to the point (5,2) along the parabola x = y² + 1.arrow_forwardEvalulate the Integral. Add +C at the end pleasearrow_forwardEvaluate the line integral f(2x-y+6)dx + (5y + 3x-6)dy, for which the path C traverses around a circle of radius 2 with centre at (0, 0) in the counterclockwise direction. Answer: (Roundarrow_forwardi dont understand 5 and 6arrow_forwardEvaluate the line integral by the two following methods. (IMAGE)arrow_forward(a) Let f(z) = (z +4- i(24 + 5z) Using CRT, evaluate the integral of(e)dz, where the contour C is the circle z + 4| = 2. z9 +5 (b) Evaluate the domain of the function h(z) = 3 %3D z2 +i Windows buii انتقل إلى الإعدادت لتند コ )园中arrow_forwardEvaluate the line integral -ydx + xdy along the curve C : y = 3x from (3, 3) to (0,0). NOTE: Enter the exact answer. -ydx + xdyarrow_forwardExpress fe Real(4i + 2iz) dz where C is the directed line segment that joins the point 3+ i to the point -2- 4i as a Riemann integral; do not evaluate it.arrow_forwardNonearrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,