Definite Integal (20 points)

2013-04-28 7:42 am
(1) Evaluate the following integrals
(a) ∫ [5+4x-x^(2)] dx
(b) ∫ (x+4) / [x^(2)+2x+5] dx
(c) ∫ (x) / [(x+2)^(3)] dx
(d) ∫ [x^(1/2)-1]^(1/2) dx
(e) ∫ [9-x^(2)] dx
( f) ∫ [x^(3)][cos(x^(2))] dx

(2) Evaluate the integral of the f(x) = I x-1 I from 0 to 4 .

(3) Evaluate the area bounded between the following curves.
C1: y = 1/x C2: y = (-3/2)x + (7/2)

(4) Find the area bounded by the parabola y^(2) = x+5 and
the straight line x-2y+2 = 0 .

(5) Find area bounded by the following curves.
C1: y = 2 + x^(2) C2: y = 5x - 4 C3: y = 2 / (1+x)

(6) Find the area of region enclosed by the given curves.
C1: y = x^(1/2) C2: y = x / 9 C3: x = 9

(7) Find the area of region enclosed by the given curves.
C1: y = cos x C2: y = sin 2x C3: x = 0 C4: x = π / 2
更新1:

你好似有好多題計錯數wo...

回答 (2)

2013-04-29 1:50 am
1(d) Let y=[x^(1/2) - 1]^(1/2)
y^2 =x^(1/2) - 1
x = (y^2 +1)^2
dx=4y(y^2 +1)dy
Integral becomes Int 4y^2(y^2 +1)dy...


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