Maharashtra State BoardHSC Commerce 12th Board Exam
Advertisement Remove all ads

Evaluate: ∫x⋅e2x dx - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Sum

Evaluate: `int "x" * "e"^"2x"` dx

Advertisement Remove all ads

Solution

Let I = `int "x" * "e"^"2x"` dx

`= "x" int "e"^"2x" "dx" - int["d"/"dx" ("x") int "e"^"2x" * "dx"]` dx

`= "x" * "e"^"2x"/2 - int 1 * "e"^"2x"/2` dx

`= 1/2 "xe"^"2x" - 1/2 int "e"^"2x"` dx

`= 1/2 "x e"^"2x" - 1/2 * "e"^"2x"/2` + c

∴ I = `1/4 "e"^"2x" ("2x" - 1)` + c

Concept: Methods of Integration: Integration by Substitution
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 5 Integration
Miscellaneous Exercise 5 | Q 4.4 | Page 139
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×