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The Fundamental Theorem of Calculus: Solve each of the following definite integrals.

  1. 11001x43dx.
  2. 0.0111x43dx.
  3. 11001x34dx.
  4. 0.0111x34dx.

Short Answer

Expert verified

The solution for the given integrals are,

Part a: role="math" localid="1649140409260" 11001x43dx2.3537.

Part b: 0.0111x43dx10.9248.

Part c: 11001x34dx2.1623.

Partd:0.0111x34dx0.6838.

Step by step solution

01

Part a Step 1. Given information

11001x43dx.

02

Part a Step 2. Now apply the fundamental theorem of calculus in the given integral

11001x43dx=11001x413dx=1100x4-13dx=x-13-131100=-3100-13-1=-3(0.2154-1)2.3537

03

Part b Step 1. Given information

0.0111x43dx.

04

Part b Step 2. Now apply the fundamental theorem of calculus in the given integral

0.0111x43dx=-3x-130.011=-31-4.641610.9248

05

Part c Step 1. Given information

11001x34dx.

06

Part c Now apply the fundamental theorem of calculus in the given interval.

11001x34dx=x141100=10214-12.1623

07

Part d Step 1. Given information

0.0111x34dx.

08

Part d Step 2. Now apply the fundamental theorem of calculus in the given interval.

0.0111x34dx=x140.011=1-1×10-2140.6838

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