Calculus II ( Engineering Analysis II)

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7nef

Mathematics

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hello, I need someone one to explain to me how did we solve these 6 questions step by step

T

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1 2. FIND THE AREA BETWEEN THE TWO CURVES y = r² +1 AND 3 - x?. USE THE GRID AS A WORK AREA TO SKETCH CURVES g 2 TX Х 2 X² + 1 = . - x 3 Х 2 2x = 2 2 -> x² =) X: t. -T A = / 92 - 9,) dx (x²41) - x - x² * dx ✓ -1 - 可 2 A A برادر ( ا --- 3) - 9 -1 X 16-2) + (122) 2 블 lo A+ [3 - - [0-4-4-) -(- - + 5 ) A. L- +3-5 - n. - 1 +2 - 2 / 2 19 A A = ३ 20 1 외 28 1 ye 3. y² = x-1 left USING THE REGION BOUNDED BY X = y +1 AND x = 3 AND y = 0. FIND VOLUME GENERATED BY ROTATING ABOUT THE X-axis. 1. Yelt ş v = π y² dx 4 V=5 / (x-1) Jx 9 2 y = X-) Х 8 V=Jy²dx v-8 [4-a], V=A[(* . - 3)-(o] Vest ( 22 ) [v. 2 / 2 B 9 = 1.55 4. FIND X OF THE CENTROID FOR THE PARABOLA Y = hr? 62 NOTE: AREA OF A PARABOLIC SECTION IS A, = {bhs XA SI я y X Х SOJA h b y x y sx 0 11 b → X bh } - b = JA-y dx 10 dx X=th ***) =) $ KX Xdx X - th 62 x= 0 56 2 X = 「 SCHO] 919 19 5. FIND 1, FOR A TRIANGULAR PLATE WHERE y = 1 AND X = 2 is BOUNDED BY THE X - axis AND THE y-axis., x ² lm / / у I (三) . y 1 S&P ly=1 I Х x² Pty Jx こ Iy 2 X y 2 dx 2 X I ㅗ Ig=pt . XIN dx 8 IS y 넝 2 2 sms pt ydx e 을 a 크 2 Iy = Pt [ ] O Iy = Pt [ 26 ) - (0) Iy? Zet 92 6. SET UP THE INTEGRAL IN TERMS OF THE VARIABLE Y TO FINDI, FOR THE CONE GENERATED BY REVOLVING THE RIGHT TRIANGLE WITH SIDES r AND h ABOUT THE x - axis. INCLUDE THE LIMITS OF INTEGRATION. (HINT: FIRST FIND AN EQUATION FOR THE LINE IN TERMS OF L AND r AND THEN USE A HORIZONTAL ELEMENT.) у 26 - y = 5 x + x tt r + dy as h - this is for Gx x x=y-r Shells Ix = y dm I = 1 yr Pe x dy I x Pt Iate ( y² ( - 1 th) dy mapor yady I.- ft -mu'. .' ) Jy = (y-7) - 2 1,= P2 [*] 1. )-(0) I, () TV14 --- x 뿐 any X = T th $ substitue for FIND THE WORK DONE IN LIFTING A 100 LB LOAD 2 FEET WITH A 10 FT CHAIN AND PULLEY IF THE CHAIN HAS A WEIGHT PER UNIT LENGTH OF 6 LBS PER FOOT. f(x) dx 2 10' W = was (160 - 6x) dx 12 를 2 - 6 2 100 # W=(160 x - sx ) w = [1308) -(0) w = 308 Ab-fft الما f(x) = 100+ (6110-x)) f(x) = loot 60 - 6x f(x) = 100 - 6x 4 5
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Explanation & Answer

Please find the word file. I have added explanation and also corrected some calculations. Please go through it and see whether you don't understand any part

Question 1:

In the above question:
The equation of top line is
Y2 = 3 – x^ 2
And the equation of bottom line is
Y1 = x^2 +1
The points where they intersect can be found by using
Y2 = y1





3 -x^2 = x^2 +1
2x^2 = 3- 1 =2
X^2 =1
X = +-1

So the area between the curve will be the area starting from x = -1 and ending at x =2 and the
equation of area is
1

A = ∫−1(𝑦2 − 𝑦1)
1

 A = ∫−1(3 − 𝑥 2 − 𝑥 2 − 1)𝑑𝑥
4
3

8

=3

Question 3 and 4:

1

2

2

2

= ∫−1(2 − 2𝑥 2 ) = [2�...


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