Show that integration of $\int {\frac{{2x + 3}}{{{x^2} + 3x}}} dx = \log \left| {{x^2} + 3x} \right| + C$ ~~~~~[NCERT Exemp. Q. 2,Page 163 ]
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Show that \[\int {\frac{{2x – 1}}{{2x + 3}}} dx = x – \log \left| {{{(2x + 3)}^2}} \right| + C\] ~~~~~[NCERT Exemp. Q. 1,Page 163 ]
Let $I = \int {\frac{{2x – 1}}{{2x + 3}}} dx = \int {\frac{{2x + 3 – 3 – 1}}{{2x + 3}}} dx$ $ = \int 1 dx – 4\int {\frac{1}{{2x + 3}}} dx = x – \int {\frac{4}{{2\left( {x + \frac{3}{2}} \right)}}} dx$ $ = x – 2\log + \left| {\left( {x + \frac{3}{2}} \right)} \right|{C^\prime } = x – 2\log \left| {\left( {\frac{{2x + 3}}{2}} \right)} \right| + {C^\prime }$ $ = x – 2\log |(2x + 3)| + 2\log 2 + {C^\prime }$ $ = x – \log \left| {{{(2x + 3)}^2}} \right| + C$ Buy Best Mathematics E-Books Visit : https://mathstudy.in/ Buy Mathematics Formula Book for Class XI,XII,JEE and other Engineering Competition Exam https://mathstudy.in/product/mathematics-formula-book/ Buy Mathematics Workbook for Class XII ( Fully Solved ) : https://mathstudy.in/product/work-book-class-xii-c-b-s-e-fully-solved/ Buy Mathematics Chapter Tests for Class XII ( Fully Solved) : https://mathstudy.in/product/mathematics-chapter-tests-class-xii-c-b-s-e/ Buy Objective Type Question Bank Class XII (Fully Solved ) : https://mathstudy.in/product/objective-type-question-bank-for-mathematics-class-xii-c-b-s-e/
Find the area of the region in the first quadrant enclosed by x-axis, line x = \sqrt 3 y and the circle x^2 + y^2 = 4[ NCERT Ex. 8.1, Q.6,Page 366]
Find the area of the region in the first quadrant enclosed by x-axis, line x = \sqrt 3 y and the circle x^2 + y^2 = 4[ NCERT Ex. 8.1, Q.6,Page 366]
Find the area of the region bounded by the ellipse x^2/4 + y^2/9 = 1, 9x^2+4y^2=36. [ NCERT Ex. 8.1, Q.5,Page 366]
Find the area of the region bounded by the ellipse x^2/4 + y^2/9 = 1, 9x^2+4y^2=36. [ NCERT Ex. 8.1, Q.5,Page 366]
Find the area of the region bounded by the ellipse x^2/16 + y^2/9 = 1, 9x^2+16y^2=144 [ NCERT Ex. 8.1, Q.4,Page 366]
Find the area of the region bounded by the ellipse x^2/16 + y^2/9 = 1, 9x^2+16y^2=144 [ NCERT Ex. 8.1, Q.4,Page 366]
Find the area of the region bounded by x^2 = 4y,y = 2,y = 4 and the y-axis in the first quadrant [ NCERT Ex. 8.1, Q.3,Page 366]
Find the area of the region bounded by ${x^2} = 4y,y = 2,$$y = 4$ and the $y$-axis in the first quadrant [ NCERT Ex. 8.1, Q.3,Page 366]
Find the area of the region bounded by y^2 = 9x,x = 2,x = 4 and the x-axis in the first quadrant. [ NCERT Ex. 8.1, Q.2,Page 365]
Find the area of the region bounded by the curve y^2 = x and the lines x = 1,x = 4 and the x-axis. [ NCERT Ex. 8.1, Q.1,Page 365]
Find the area of the region bounded by the curve y^2 = x and the lines x = 1,x = 4 and the x-axis. [ NCERT Ex. 8.1, Q.1,Page 365]
Find the area of the region bounded by the curve ${y^2} = x$ and the lines $x = 1,x = 4$ and the $x$-axis. [ NCERT Ex. 8.1, Q.1,Page 365]
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