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2.1 Übungen

Aus Online Mathematik Brückenkurs 2

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===Exercise 2.1:1===
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===Übung 2.1:1===
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Interpret each integral as an area, and determine its value.
Interpret each integral as an area, and determine its value.
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===Exercise 2.1:2===
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===Übung 2.1:2===
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Calculate the integrals
Calculate the integrals
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===Exercise 2.1:3===
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===Übung 2.1:3===
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Calculate the integrals
Calculate the integrals
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===Exercise 2.1:4===
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===Exercise 2.1:5===
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Calculate the integral
Calculate the integral

Version vom 13:23, 10. Mär. 2009

       Theory          Übungen      

Übung 2.1:1

Interpret each integral as an area, and determine its value.

a) 2−12dx  b) 01(2x+1)dx 
c) 02(3−2x)dx  d) 2−1xdx 

Answer | Solution a | Solution b | Solution c | Solution d

Übung 2.1:2

Calculate the integrals

a) 02(x2+3x3)dx  b) 2−1(x−2)(x+1)dx 
c) 49x−1xdx  d) 14x2xdx 

Answer | Solution a | Solution b | Solution c | Solution d

Übung 2.1:3

Calculate the integrals

a) sinxdx  b) 2sinxcosxdx 
c) e2x(ex+1)dx  d) xx2+1dx 

Answer | Solution a | Solution b | Solution c | Solution d

Übung 2.1:4

a) Calculate the area between the curve y=sinx and the x-axis when 0x45.
b) Calculate the area under the curve y=−x2+2x+2 and above the x-axis.
c) Calculate the area of the finite region between the curves y=41x2+2 and y=8−81x2 (Swedish A-level 1965).
d) Calculate the area of the finite region enclosed by the curves y=x+2y=1 and y=x1.
e) Calculate the area of the region given by the inequality, x2yx+2.

Answer | Solution a | Solution b | Solution c | Solution d | Solution e

Übung 2.1:5

Calculate the integral

a) dxx+9−x  (Hint: multiply the top and bottom by the conjugate of the denominator)
b) sin2x dx  (Hint: rewrite the integrand using a trigonometric formula)

Answer | Solution a | Solution b

Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/2.1_%C3%9Cbungen“