INDIAN INSTITUTE OF SPACE SCIENCE AND TECHNOLOGY
THIRUVANANTHAPURAM 695 547
Assignment∗
MA111 - Calculus
1. Using Riemann sum, evaluate the integral R2
1x(x−2) dx.
2. Express the following limit as a Riemann sum of a definite integral and evaluate it:
limn→∞ Pn
k=1
n
k2+n2
3. Find the area of the region bounded by the curves y=x2and y=−x.
4. Find the volume of the solid obtained by rotating the region bounded by y=x2and
y=xabout the y-axis.
5. Find the area of the surface of revolution generated by rotating the curve y=x3
√3from
x= 0 to x= 1 about x-axis.
6. Use trapezoidal rule with n= 4 to estimate the integral and also find an upper bound
for the error. Z2
0
(x3+x)dx.
7. Evaluate ZDZe−(x2+y2)dxdy using polar coordinates, where Dis the region bounded
by the circle x2+y2= 16 in the first quadrant.
8. Using double integral find the volume of the tetrahedron bounded by the coordinate
planes and the plane z= 6 −2x+ 3y.
9. Find the volume of the solid generated by revolving the region bounded by y=x2and
y= 2xabout the y-axis.
10. Find the area between the parabola y= 4x−x2and the line y=xusing double
integral.
11. Evaluate Z1
0Z1
y
ex2dxdy.
(Hint: use change of coordinates).
* Last date to submit the assignment - 27-2-2022.
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