Use areas to evaluate the integral f(x)= 7x+ 25 - xon the following intervals. (a)(-5.0] (b)(-5.5)...
Evaluate the following integral using trigonometric substitution. 7x² dx (121 + x2) 7x² dx s (121 +x?)? (Type an exact answer.)
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. f(xyz) = 4x, where S is the cylinder X + z2-25, 0 ys2 The value of the surface integral is (Type exact answers, using T as needed.) Find the area of the following surface using the given explicit description of the surface. The cone z2 = (x2 +y2) , for Oszs8 Set up the surface integral for the given function over the given surface S as a...
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. 2 f(x,y,z) x 2 where S is the hemisphere x + y +z2 = 25, for z 2 0 The value of the surface integral is (Type an exact answers, using t as needed.)
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. 2 f(x,y,z) x 2 where S is the hemisphere x + y +z2 = 25, for z 2 0 The...
Evaluate the line integral ſ vydr for the following function s and oriented curve C (a) using a parametric description of C and evaluating the integral directly, and (b) с using the Fundamental Theorem for line integrals XY.2) - * 7x for sts 4 4 2 C: (0 cost, sint, Uning either methods, ſv • dr - C (Type an exact answer
12.5.10 Answer the following questions about F(x)-7x+110. (A) Calculate the change in F(x) from x- 10 to x-17. (B Graph F and use geometric formulas to calculate the area between the graph of F and the x-axis from x (C) Verity that your answers from (A) and (B) are equal, as guaranteed by the fundamental theorem of calculus. 10 to x=17. (A) Calculate the change in F(x) from x 10 to x - 17. The change is© Simplify your answer.)...
please answer all 3 questions, I need help. thank you
Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise. $(9x+ ex) dy- (4y + sinh x) dx, where C is the boundary of the square with vertices (2, 0), (5, 0), (5, 3), and (2, 3). $(9x+ ey?) ay- (4y+ + sinhx) dx = 0 (Type an exact answer.) Use Green's Theorem to evaluate the following line integral. i dy - g dx, where (19)...
Evaluate the line integral in Stokes Theorem to evaluate the surface integral J J(VxF)-n ds. Assume that n points in an upward direction F (xty,y z,z+x) S is the tilted disk enclosed by r()-(3 cost,4sint,7 cos t Rewrite the surface integral as a line integral. Use increasing limits of integration. dt (Type exact answers, using π as needed.) Find the value of the surface integral. JÍs×F).nds-ロ (Type an exact answer, using π as needed.)
Evaluate the line integral in Stokes...
EXAMPLE 4 Evaluate the following integrals by interpreting each in terms of areas. (a) y=V25-2 lov ✓ 25 - 2 dx or 10 + y = 25 (x - 3) dx SOLUTION (a) Since Rx) = V25 - x2 > 0, we can interpret this integral the area under the curve y = 25 - X2 from 0 to But we get x2 + y2 = 25, which shows that the graph of ris a quarter-circle with radius in the...
Evaluate the integral below by interpreting y=f(x) it in terms of areas in the figure. A1 АЗ The areas of the labeled regions are 10 31 5 A2 7A4 10 A1= 7, A2=4, A3=2 and A4=2 (figure is NOT to scale) v= 5.5" f(a)de V = Enter your answer as a whole number
The graph of f is shown. Evaluate each integral by interpreting it in terms of areas.(a) \(\int_{0}^{10} f(x) d x\)(b) \(\int_{0}^{25} f(x) d x\)(c) \(\int_{25}^{35} f(x) d x\)(d) \(\int_{0}^{45} f(x) d x\)