21bw08mt2asolns2

21bw08mt2asolns2 - MAT 21B Midterm IIa Name: Student Id:...

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Unformatted text preview: MAT 21B Midterm IIa Name: Student Id: Section: No notes. No calculators. All incidents of cheating or the appearance thereof will be brought to the attention of Student Judicial Affairs. 1) 2) 3) 4) 5) Total (out of 50): 1 1) (True/False) Label the following statements as either true or false. (No explanation required. Each correct label is worth two points.) a: If u = g ( x ) is a differentiable function and f is continu- ous, then integraldisplay f ( g ( x )) f ( x ) dx = integraldisplay f ( u ) du. False. integraldisplay f ( g ( x )) g ( x ) dx = integraldisplay f ( u ) du. b: sec (2 x ) = 2 sec ( x ) False. sec (2 ) = 1 cos(2 ) = 1 1 negationslash = 2 1 ( 1) = 2 1 cos( ) = 2 sec( ) c: integraldisplay 4 2 dx xlnx = ln 4 ln 2 True. Let u = ln x . Then du = 1 x dx , so integraldisplay 4 2 dx xlnx = integraldisplay u =ln 4 u =ln 2 1 u du = ln u | u =ln 4 u =ln 2 = ln(ln 4) ln(ln 2) = ln parenleftBigg ln 4 ln 2 parenrightBigg = ln ln 2 2 ln 2 = ln parenleftBigg 2 ln 2 ln 2 parenrightBigg = ln 2 And, ln 4 ln 2 = ln 2 2 ln 2 = 2 ln 2 ln 2 = ln 2 2 d: The center of mass of a square plate of constant density...
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21bw08mt2asolns2 - MAT 21B Midterm IIa Name: Student Id:...

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