The following surface integral is to be evaluated over a sphere for the given steady vector field, F = xi + yj + zk defined with respect to a Cartesian coordinate system having i, j, and k as unit base vectors.
, Where S is the sphere, x2 + y2 + z2 = 1 and n is the outward unit normal vector to the sphere. The value of the surface integral is
The value of the integral , where D is the shaded triangular region shown in the diagram, is _____ (rounded off to the nearest integer).
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A definite double integral is given below, then, evaluation of the double integral over the region R will be __
Where R is the region on X - Y plane for the function given as, and r ∈ [0, 5]
The integral , where D denotes the disc 2 + 2 ≤ 4, evaluates to__________.
The area bounded by the curves y2 = 9x, x – y + 2 = 0 is given by
Let , where R is the region shown in the figure and c = 6 × 10-4. The value of I equals________. (Give the answer up to two decimal places.)
An ellipse is revolved around the y-axis. The volume generated by the solid of revolution if a = 3 and b = 2 is______
The value of , where dA indicate small area in xy - plane, is
65 videos|120 docs|94 tests
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65 videos|120 docs|94 tests
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