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2.1 Übungen

Aus Online Mathematik Brückenkurs 2

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Exercise 2.1:1

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

a) 212dx  b) 01(2x+1)dx 
c) 02(32x)dx  d) 21xdx 

Exercise 2.1:2

Calculate the integrals

a) 02(x2+3x3)dx  b) 21(x2)(x+1)dx 
c) 49x1xdx  d) 14x2xdx 

Exercise 2.1:3

Calculate the integrals

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

Exercise 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=881x2 (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.

Exercise 2.1:5

Calculate the integral

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