Web view1+ 4 x 2 dx= 1 2 sec 3 θdθ .Question IV. Evaluate . f'(0) for . f x = tanh -1 5...
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Transcript of Web view1+ 4 x 2 dx= 1 2 sec 3 θdθ .Question IV. Evaluate . f'(0) for . f x = tanh -1 5...
King Saud University Math 106Science and Medical Studies Section for girls First Term 1432-33HCollege of Science Second Midterm ExamDepartment of Mathematics 105 Minutes
Name: Student No.:
Section No.: Staff member name:
Question No I II III IV TotalMark
Question IEvaluate the following integrals:
1) ∫0
sinh3 1√1+x2
dx
2) ∫0
∞ x(1+x2)2
dx
1
3) ∫ (lnx )2dx
4) ∫ 3x2−4 x+8
dx
5) ∫cos3x √sinx dx
2
Question II
1) Use the substitution u=x2+1 to prove that
∫ 2x3+ x
dx=∫ 1u (u−1 )
du.
2) Compute ∫ 1u(u−1)
du.
3) Conclude ∫ 2x3+ x
dx.
3
Question III
Use an appropriate trigonometric substitution to show that
∫√1+4 x2dx=12∫ sec3θdθ.
Question IV1) Evaluate f ' (0) for f ( x )=tanh−15 x.
4
2) Determine whether the improper integral ∫0
π
sec2 xdx converges or diverges.
Good Luck
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